Engineering; GK & Definition of Physics, Chemistry, Mathematics Laws : Live Science

Education system GK current Affairs knowledge

2020-02-10T19:15:00.003+05:30

Education system GK current Affairs knowledge:-

१. 35 वीं सीनियर वुमन नेशनल वेटलिप्फैटिंग चैम्पियन कहा आयोजित हुई ?
a. जयपुर
b. लखनऊ
c. कोलकाता
d. गुवाहटी

२. इंडिया इंटरनेशनल सीफूड शो 2020 का आयोजन किस शहर में किया जा रहा है ?
a. विशाखापटनम
b. मुंबई
c. कोच्चि
d. चेन्नई

३. UAE की जीडीपी का........ प्रतिशत आयल और गैस पर निर्भर है।
a. 25
b. 30
c. 35
d. 405

४. किस राजय की कैबिनेट ने सुन्नी वक्फ बोर्ड को 5 एकड़ भूमि दिए जाने के प्रस्ताव की मंज़ूरी है ?
a. महराष्ट्र
b. उत्तर प्रदेश
c. मध्यप्रदेश
d. उत्तराखंड

५. जान सेवक योजना क शुरुवात किस राजय ने की है ?
a. कर्णाटक
b. महराष्ट्र
c. आंध्रप्रदेश
d. असम

६. इंटरनेशन इन्टलेक्चुल प्रॉपर्टी इंडेक्स 2019 में भारत का कौन सा स्थान रहा ?
a. 23 वां
b. 36 वां
c. 40 वां
d. 15 वां

७. कुछ रोग निवारक के लिए किये गए प्रयास के लिए किसे इंटरनेशन गांधी अवार्ड से सम्मनित किया गया है ?
a. डॉ. रेणुका रामकृष्णन
b. प्रियंवदा चुग
c. डॉ. राम मलकानी
d. डॉ. NS धर्म शक्तु

८. राष्ट्रीय वयोश्री योजना की शुरुआत कब की गई थी ?
a. 2015
b. 2016
c. 2017
d. 2018

९. किस राज्य में भारत सरकार वधवन पोर्ट की स्थापना करने जा रही है ?
a. केरल
b. पश्चिम बंगाल
c. महाराष्ट्र
d. तमिलनडु

१०. High energy material research laboratory कंहा स्थित है ?
a. पुणे
b. बेंगलुरु
c. नई दिल्ली
d. अहमदाबाद

११. क्रूड की माप की जाती है ?
a. बैरिल प्रतिदिन से
b. गैलन प्रतिमिनिट से
c. बैरल प्रति स्ट्रीम दिन से
d. बैरल प्रतिघंटा से

१२. डिफेंस एक्सपो 2020 भारत का...... संस्करण है।
a. 10 वां
b. 11 वां
c. 12 वां
d. 13 वां

१३. भारत का पहला इंटीग्रेटेड स्टील कहा स्थापित किया गया है ?
a. भिलाई
b. दुर्गपुर
c. बोकारो
d. रावउकेला

१४. जी-7 समिट का आयोजन कब किया जायेगा ?
a. 10 जून 2020
b. 11 जुलाई 2020
c. 12 जून 2020
d. 10 जुलाई 2020

१५. अमिताभ भट्ट को......... नियुक्त किया गया है।
a. एडमिनिस्ट्रेटिव आफिसर
b. चीफ एग्जिक्यूटिव ऑफिसर
c. चीफ फाइनेंशियल ऑफिसर
d. चीफ ऑपरेटिंग ऑफिसर

Ans 1c,2c,3c,4b,5a,6c,7d,8c,9c,10a,11a,12b,13d,14,15b.

The First National Bird in The World

2019-12-14T08:36:00.000+05:30

The First National Bird in The World:-

On July 4, 1776, the Second Continental Congress of the United States issued the declaration of independence and decided that the new United States must have a special national emblem. On June 20, 1782, the Congress of the United States passed a resolution to regard the unique white headed sea sculpture of North America as the national bird of the United States, and take this bird as the main body of the national emblem pattern. It is the first "national bird" in the world.White headed sea eagles are popular with the American people because of their North American landmarks and vigorous posture. Today, the image of white headed sea eagles can be seen everywhere in the United States.

White headed sea eagles, also known as white headed eagles, bald eagles, American Eagles and American Eagles, are a kind of raptors in North America. Their active areas are usually in open water areas, and their food is mainly fish. However, they also hunt different prey according to different environments. The white headed sea eagle is the national bird of the United States and one of the most important symbols of the United States.

White headed sea eagles prefer to live near the coast, rivers and lakes, because there are many fish in these places, which are very rich food resources for them. Research shows that they prefer rivers with a circumference of more than 11 kilometers, and lakes with an area of more than 10 square kilometers are the most suitable for white headed sea eagles in breeding period. White headed sea eagles are good at flying. They can fly at speeds of 56 to 70 kilometers per hour when gliding and flapping their wings. If they catch fish in flight, they can still fly at speeds of 48 kilometers per hour.

People who have seen the white headed sea sculpture will be attracted by its powerful appearance and vigorous posture. Its body length can reach one meter, its wingspan can exceed two meters, and it weighs 3 to 6 kilograms. Its average life span is about 20 years, but it's not uncommon to live to 40-50 years old. White headed sea eagles have bright yellow eyes, beaks and claws. Adult white headed sea eagles, both male and female, are covered with brown feathers, but the head, neck and tail are white feathers.

Interestingly, the English name of the sea eagle with white head is bald eagle, which is translated as "vulture". This is probably because it is white from the forehead to the neck. At a glance, it will think that it is "bald". In fact, it is only "white head", not "bald head".

The milky way is a Spiral Galaxy

2019-12-13T12:26:00.002+05:30

The milky way is a Spiral Galaxy -

After 75 years of research, radio, infrared and even x-ray telescopes have confirmed their existence, and found that the spiral cloud extends 100000 light-years (the diameter of the disk), with a thickness of 1000 light-years (the thickness of the disk). On this gorgeous disk, our tiny solar system lies on the inner edge of an arm, about 25000 light-years from the center.

Human beings determining the shape of the galaxy is like that a microorganism determines the shape of the earth. We can't get a good location to identify it, because this location must exist outside the galaxy. But looking at it from the outside of the galaxy gives you an overall picture of it.

In an area free from air pollution, the Milky way can be seen with the naked eye. When enjoying the beautiful scenery, the observer will notice that the twinkling stars are arranged in a narrow strip area through the darkness. There is a fuzzy bulge between this area, which is wider than the ribbon area on both sides. The appearance of such a compressed band of stars shows that we are looking at the side of a disk. The Milky way is a flat disk in which the bulge is the center of the galaxy.

Also, when we locate stars and measure their velocities, we find that this vector has a rotation component different from that of random motion. This is the characteristic of spiral galaxies. A star like the sun is formed when a huge dense cloud of hydrogen gas gathers under gravity. The remaining hydrogen dust or gas is dispersed by the new star flare. When the cloud interacts with light, it randomly scatters photons and creates light spots near the star. We can locate stars by searching for these spots, which are sun care landmarks. When astronomers located these points, they found that stars were focused on spiraling branches of light protruding from the center. We call these spiral branches "spiral arms" of spiral galaxies.

We study the properties of other spiral galaxies, such as the dust content, the order of stars and their speed, and compare them with our galaxy. Obviously, these findings are like the appearance of twins, with flat disks, gas friction, color and dust content shared by all spiral galaxies.

"Flower" in The Universe

We often see beautiful nebulae in satellite pictures of the universe. So what is a nebula? According to the scientists, a nebula is a kind of gas. It is usually composed of dust, hydrogen, helium and other ionized gases, just like the rainbow we see on earth.

So, some friends are curious, the universe does not exist in a void environment, why are nebulae? In fact, the nebula is not visible alone, and the universe is not without a minor gas, the nebula is through a universe of little gas and dust, slowly building an object that we now together to form a cloud lets see. - Nebula.

The trend of nebula is very large. The nebulae we see with our detectors are usually tens of light years in size, and as the name suggests, they are very low in density, like clouds on our planet, floating in space. The nebula is closely related to stars and, as described above, are clusters of dust and gas.

In fact, the nebula is not only beautiful, large nebulae are often accompanied by the birth of stars, once the size of the nebula, will continue to squeeze together, gradually forming a giant form. Increasing gravity will attract millions of millions of years or more of dust, gases and other substances, which we know are larger in size.

And the beautiful nebulae that we see, most of the planetary nebulae, are due to the fact that the center of the nebulae, or nearby, has glowing stars that reflect and refract light through the nebulae. As early as 1758, nebulae were discovered by a French astronomer, because of its unique characteristics, named nebulae, we also through the characteristics of nebulae glow, the nebulae into luminous gas clouds, dark nebulae, reflection nebulae and emission nebulae.

Stars Milky Way and colorful nebulae decorate the universe so beautifully and also enhance man's determination to explore the universe. When we look at the entire universe, the more mystery we discover, the more mysterious it feels to us, and the more awe we have. In the future, with the development of anthropology and technology, we may get more secrets!

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Mobile phone high quality wallpaper

2019-12-13T12:00:00.000+05:30

दुनिया की सबसे पहली N. के Pilot कौन थे ? ( Who was the world's first pilot ? )

2019-11-24T13:35:00.003+05:30

दुनिया के सबसे पहले न. के पॉलेट कौन थे ???👇👇👇

अगर आप नहीं जानते तो आपको बता दे कि दुनिया के सबसे पहले न. के पाइलेट Mr. Wili third man
जिनकी जन्म 22 नवम्बर, सन्न 1898 में हुवा था !

अगर आप यह भी नहीं जानते की भारत की सबसे पहली पॉयलेट कौन थे ? तो जान लीजिये भारत के सबसे पहले पॉलेट जहांगीर रतनजी दादाभाई (जेआरडी) टाटा है

नई दिल्लीः
आज टाटा ग्रुप के जहांगीर रतनजी दादाभाई (जेआरडी) टाटा का जन्मदिन है। टाटा...यह नाम आज किसी पहचान का मोहताज नहीं है। एक ऐसी कंपनी जिसका दखल नमक से लेकर आई.टी. कंपनी और जगुआर लैंड रोवर जैसी लग्जरी कार तक है। यह कंपनी रातोरात इतनी बड़ी नहीं बनी। इसके पीछे जेआरडी की कड़ी मेहनत का हाथ है। जानिए जेआरडी टाटा से जुड़ी कुछ खास बातें-

1938 में 34 साल की उम्र में ही उन्होंने अपने पिता के कारोबार की कमान संभाल ली। उनकी शानदार लीडरशिप में टाटा ने जिस कारोबारी ऊंचाई को छुआ, उसका अंदाजा आप इस आंकड़े से लगा सकते हैं। 1939 में टाटा की नेटवर्थ 62 करोड़ रुपए थी जो बढ़कर 1990 में 10,000 करोड़ रुपए हो गई। आज टाटा की नेटवर्थ 104 अरब डॉलर है।

देश के पहले लाइसेंसी पायलट

जेआरडी के पिता रतनजी दादाभाई टाटा पारसी थे। जेआरडी का जन्म 1904 में पेरिस में हुआ था। जेआरडी की परवरिश फ्रेंच मां और पारसी पिता के बीच हुई। उनका शुरुआती जीवन फ्रांस में बीता था। 1914 में हुए प्रथम विश्व युद्ध के दौरान उन्होंने 1 साल तक सिपाही की हैसियत से फ्रांस के लिए युद्ध भी किया। उनका ताल्लुक एक ऊंचे खानदान से था।

उनकी मां सुजैन आरडी टाटा कार चलाने वाली भारत की पहली महिला थीं। खुद जेआरडी देश के पहले लाइसेंसी पायलट थे। उन्हें 1929 में लाइसेंस मिला था। जेआरडी को इंडियन सिविल एविएशन का पिता भी कहा जाता है। बहुत कम लोगों को इसकी जानकारी है कि एयर इंडिया की शुरुआत जेआरडी ने ही की थी। फ्रांस में कुछ साल बिताने के बाद वह लंदन चले गए और फिर भारत आ गए। और यहां से एक बिजनेस के तौर पर टाटा का सफर शुरू हुआ।
कंपनी को पहुंचाया ऊंचाईयों तक

अंतिम समय
जेआरडी की मौत 29 नवंबर 1993 को गुर्दे में संक्रमण के कारण जिनेवा में हुई। उनकी मृत्यु पर भारतीय संसद उनकी स्मृति में स्थगित कर दी गई थी। उनको पेरिस में पेरे लेचसे नामक कब्रिस्तान में दफनाया गया है। कंपनियों में एच.आर. की शुरुआत उन्होंने ही की थी। आज किसी कंपनी में एचआर होना भले ही सामान्य बात है लेकिन उस वक्त यह नौकरी करने वालों के लिए क्रांति थी। जेआरडी चाहते थे कि भारत सबसे खुशहाल देश बने। हालांकि उनका यह सपना तो पूरा नहीं हो पाया लेकिन टाटा एक भरोसेमंद कंपनी जरूर बन चुकी है।

दुनिया का सबसे बड़ी हवाई दुर्घटना 1977 में हुई थी। यह दुर्घटना दो हवाई जहाज़ के टकराने से हुई थी, जिसमे 500 यात्री की दुर्घटना हुई थी।

आपको बता दे की दुनिया की सबसे तेज उड़ने वाली हवाई जहाज़ the concorde airplane ब्रिटिश ऑफ़ फ़्रांस ने मिलकर बनाया था इसकी स्पीड करीबन 2180 km/h है।

क्या आपको पता है की, हवाई की टायर में कितने प्रेस्सर का हवा डाला जाता है , कई लोगो का मानना है की लैंडिंग के तुरंत बाद टायर बदल दिया जाता है, लेकिन ऐसा होता कुछ भी जब ज़रूरत पड़ता है तब टायर बदला जाता है। 200 PSI Pressure का एयर भरा जाता है। यदि हवाई 180 km/h के स्पीड भी लैंडिंग तो भी टायर में कोई नुकसान नहीं होगा ,

कई लोगो की मनना है की उनकी सैलरी हवाई जहाज़ उड़ने के नहीं देते होंगे पर बात कुछ और ही है।
आपको बता दे की एक पायलेट की सैलरी उसके महीने के हिसाब से नहीं होता बल्कि उनको हवाई जहाज़ के घंटो के हिसाब से दिया जाता है ,

क्या आपको क्या आपको पता है कि दुनिया की सबसे लंबी हवाई जहाज यात्रा BELUGA AIRBUS A380 यह हवाई जहाज 27 अप्रैल 2005 में बनाया गया था

SIMPLIFICATIO सरलीकरण

2019-11-10T15:33:00.001+05:30

सरलीकरण
समान्य नियम

ध्यान रहे कि विभिन्न संक्रियाओं को केवल निम्न क्रमानुसार लेते है

प्रश्न, १

sol.

दिया गया यंजक

प्रश्न, २
ममता के पास 100 रु तथा 50 रु के कुल 85 नोट है जिनका कुल मूल्य 5000 है, इनमें से 50 रु के नोट कितने हैं ?

sol.
माना 50 रु के नोटो की संख्या = x

तब, 100 रु के नोटों की संख्या = (85-x)

50x =(8500-5000)=5000

50x=(8500-5000)=3500

x=70

50 रु के नोटों की संख्या = 70 .Ans

प्रश्न. 3. PDf file download click

De broglie wavelength equation (De-Broglie equation )

2019-11-10T14:27:00.002+05:30

De Broglie Wavelength Formula

In some situations, light behaves like a wave, while in others, it behaves like particles. The particles of light are called photons, and they can be thought of as both waves and particles. Louis de Broglie (1892-1987) developed a formula to relate this dual wave and particle behavior. It can also be applied to other particles, like electrons and protons. The formula relates the wavelength to the momentum of a wave/particle.

For particles with mass (electrons, protons, etc., but not photons), there is another form of the de Broglie wavelength formula. At non-relativistic speeds, the momentum of a particle is equal to its rest mass, m, multiplied by its velocity, v.

The unit of the de Broglie wavelength is meters (m), though it is often very small, and so expressed in nanometers (1 nm = 10(-9) m), or Angstroms

De broglie wavelength equation (De-Broglie equation )

In 1924, Louis de-Broglie give the idea that matter should also posses dual nature. According to Louis de-Broglie a moving matter particle is surrounded by a wave whose wavelengths depend upon the mass of the particle and its velocity. These waves associated with the matter particles are known as matter waves or de-Broglie waves. The wavelength of the particle can be find through the following relation -

where h is the Planck's constant and p is the momentum of particle. The value of Planck's constant is

The de-Broglie concept of matter waves was based on the following facts-

(i) Matter and light, both are forms of energy and each of them can be transformed into the other.

(ii) Both are governed by the space time symmetries of the theory of relativity.

Derive an expression for the de broglie wavelength:-

Considering the Planck's theory of radiation, the energy of the a photon (quantum) is given by

......(1)

where c is the velocity of light in vacuum and is its wavelength.

According to Einstein energy mass relation

........(2)

From equation (1) & (2), we get

........(3)

where mc = p (momentum associated with photon).

If we consider the case of a material particle of mass m and moving with a velocity v, then the wavelength associated with this particle is given by

..........(4)

If E is the kinetic energy of the material particle then

.........(5)

Substituting the value of p in equation (4), we get de broglie wavelength,

...........(6)

According to kinetic theory of gases, the average kinetic energy of particle is given by

where, K= Boltzmann's constant =

Putting the value of E in equation (4)

Home rothery's rules and regulations (physics)

2019-10-15T21:22:00.002+05:30

Hume-Rothery rules:-

HUME-ROTHERY'S RULES:-

In the course of an alloy development, it is frequently desirable to increase the strength of the alloy by adding a metal that will form a solid solution. In the choice of such alloying elements, a number of rules govern the for- mation of substitutional work of Hume-Rothery. Unfortunately, if an alloying element is chosen at random, intermediate phase instead of a solid solution.

Hume-Rothery's Rules are described below. is likely to form an objectionable.

👇👇👇👇👇👇👇👇👇👇👇👇👇

CHEMICAL AFFINITY FACTOR

The greater the chemical affinity of two metals the more restricted is their solid solubility. When their chemical affinity is great, two metals tend to form an intermediate phase rather than a solid solution.

Chemical Affinity Factor-The greater the chemical affinity of two metals, the more restricted is their solid solubility. When their chemical affinity is great, two metals tend to form an intermediate phase rather than a solid-solution. Generally, the farther apart the elements are in the periodic table, the greater is their chemical affinity.

RELATIVE VALENCY FACTOR

If the alloying element has a different valence from that of the base metal, the number of valence electrons per atom, called the electron ratio, will be changed by alloying. Crystal structures are more sensitive to a decrease in the electron ratio than to an increase. Therefore, a metal of high valence can dissolve only a small amount of lower valance metal, while the lower valence metal may have good solu- bility for a higher valence metal.

Relative Valence (Valency) Factor - It has been found that the metal of high valence can dissolve only a small amount of a lower valence metal, while the lower valence metal may have good solubility for the higher valence metal. For example in the Al-Ni alloy system both metals have FCC structure. The relative size factor is approximately 14%. However, Ni is lower n valence than Al and thus solid nickel dissolves 5% aluminium, but the higher valence Al dissolves only 0.04% Ni.

RELATIVE SIZE FACTOR

If the size of two metallic atoms (given approxima- tely by their constants) differs by less than 15 percent, the metals are said to have a favourable size factor for solid solution formation. So far as this factor is concerned, each of the metals will be able to dissolve apprecia- bly (to the order of l0%) in the other metal. If the size factor is greater than 15°, solid solution formation tends to be severely limited and is usually only a fraction of one percent.

Relative Size Factor- If the two metals are to exhibit extensive solid solubility in each other, it is essential, that their atomic diameters shall be fairly similar, since atoms differing greatly in size cannot be accommodated readily in the same structure (as a substitutional solid solution) without producing excessive strain and corresponding instability. This is what referred as the term size factor. The extensive solid solubility is encountered only when the two different atoms differ in size by less than 15%, calleda favourable size factor (e.g. Cu-Ni, Au-Pt). If the relative size factor is between 8% and 15 % , the alloy system usually shows a minimum and if this is greater than 15 % , substitutional solid solution formation is very limited.

LATTICE-TYPE FACTOR

Only metals that have the same type of lattice (FCC for example) can form a complete series of solid solutions. Also, for com- plete solid solubility, the size factor must usually be less than 8 percent. Copper-nickel and silver-gold-platinum are examples of binary and ter- nary systems exhibiting complete solid solubility.

Crystal Structure Factor The crystal lattice structure of the two elements (metal) should be same (i.e. both should be of BCC, FCC, or HCP structure) for complete solubility, otherwise the two solutions would not merge into each other. Also for complete solid solubility the size must usually be less than 8%.

HINDI TRANSLATE👇👇

Hume-Rothery's Rules are described below. is likely to form an objectionable.

रासायनिक प्रभाव क्षेत्र

दो धातुओं का रासायनिक आत्मीयता जितना अधिक प्रतिबंधित है, उनकी ठोस घुलनशीलता है। जब उनकी रासायनिक आत्मीयता महान होती है, तो दो धातुएं एक ठोस समाधान के बजाय एक मध्यवर्ती चरण बनाती हैं।

रिश्ता वैधता का कारखाना

यदि मिश्र धातु तत्व का आधार धातु से भिन्न भिन्नता है, तो प्रति परमाणुओं में वैलेंस इलेक्ट्रॉनों की संख्या, जिसे इलेक्ट्रॉन अनुपात कहा जाता है, को मिश्रधातु द्वारा बदल दिया जाएगा। वृद्धि की तुलना में क्रिस्टल संरचनाएं इलेक्ट्रॉन अनुपात में कमी के प्रति अधिक संवेदनशील हैं। इसलिए, उच्च वैलेंस की एक धातु केवल कम वैलेंस धातु को भंग कर सकती है, जबकि कम वैलेंस धातु में उच्च वैलेंस धातु के लिए अच्छा सॉल्यू-बाइट हो सकता है।

विश्वसनीय आकार फैक्टरी

यदि दो धात्विक परमाणुओं का आकार (उनके स्थिरांक द्वारा अनुमानित रूप से दिया गया) 15 प्रतिशत से कम होता है, तो धातु को ठोस घोल बनाने के लिए अनुकूल आकार कारक कहा जाता है। जहाँ तक इस कारक का संबंध है, प्रत्येक धातु दूसरे धातु में apprecia- bly (l0% के क्रम में) को भंग करने में सक्षम होगी। यदि आकार का कारक 15 ° से अधिक है, तो ठोस समाधान गठन गंभीर रूप से सीमित हो जाता है और आमतौर पर केवल एक प्रतिशत का एक अंश होता है।

लेटिस-टाईप फैक्टर

केवल धातुएँ जिनमें एक ही प्रकार की जाली होती है (उदाहरण के लिए FCC) ठोस समाधानों की एक पूरी श्रृंखला बना सकती है। इसके अलावा, कॉम-पिल सॉलिड सॉल्युबिलिटी के लिए, साइज फैक्टर आमतौर पर 8 प्रतिशत से कम होना चाहिए। कॉपर-निकेल और सिल्वर-गोल्ड-प्लैटिनम बाइनरी और टेर-नैरी सिस्टम के उदाहरण हैं जो पूर्ण ठोस घुलनशीलता प्रदर्शित करते हैं।

CONTINUOUS CASTING PROCESS (Asarco Process)

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Continuous casting process:-

In Continuous casting process the forming die is an integral part of the furnace and thus there is no problem of controlling the flow of metal . The metal is fed by gravity into the mould from the furnace as it is continuously solidified and withdrawn by the rolls below . The die is water cooled and self lubricating and thus has excellent resistance to thermal shocks . The upper end of the die is in molten metal and thus serves the function of riser and acts as path for dissipation of evolved gases .
At the time of starting , a similar rod is put into the die till its upper end melts and forms Holding continuity with molten metal , and it is then Furnace withdrawn by rolls and the process becomes continuous . By this process , rounds , tubes , squares and special shapes can be conveniently produced and it is particularly suited to alloys like phosphorised copper and standard bronzes .

The physical properties of castings Casting - produced are superior to other processes . In continuous casting , solidifying zone being relatively small , practically all problems encountered with feeding and shrinkage are overcome . Problems due to fast cooling in mould zone are faced segregation and cracking ) . A greater degree of control is required in comparison batch casting . Asarco process is shown n fig.

Uses - Continuous casting process is specially suited to rounds , tubes , squares and special shapes , particularly made from alloys like phosphorized popper and standard bronzes .

Merits - ( i ) Physical properties of castings produced are superior to other processes , because metal is protected from contamination , while melting and being poured .

Examples of differential equations with solutions

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“Ordinary Differential Equations:-

In mathematics, the term “Ordinary Differential Equations” also known as ODE is a relation that contains only one independent variable and one or more of its derivatives with respect to the variable. In other words, the ODE’S is represented as the relation having one real variable x, the real dependent variable y, with some of its derivatives.

Y’,y”, ….yn ,…with respect to x.

The order of ordinary differential equations is defined to be the order of the highest derivative that occurs in the equation. The general form of n-th order ODE is given as;

F(x, y,y’,….,yn ) = 0

Note that, y’ can be either dy/dx or dy/dt and yn can be either dny/dxn or dny/dtn.

An n-th order ordinary differential equations is linear if it can be written in the form;

a0(x)yn + a1(x)yn-1 +…..+ an(x)y = r(x)

(The function aj(x), 0≤j≤n are called the coefficients of the linear equation. The equation is said to be homogeneous if r(x)=0.If r(x)≠0 , it is said to be a non- homogeneous equation. Also, learn the first order differential equation here.)

Ordinary Differential Equations Types

The ordinary differential equation is further classified into three types. They are:

Autonomous ODE
Linear ODE
Non-linear ODE

Autonomous Ordinary Differential Equations

A differential equation which does not depend on the variable, say x is known as an autonomous differential equation.

Linear Ordinary Differential Equations

If differential equations can be written as the linear combinations of the derivatives of y, then it is known as linear ordinary differential equations. It is further classified into two types,

Homogeneous linear differential equations
Non-homogeneous linear differential equations

Non-linear Ordinary Differential Equations

If differential equations cannot be written in the form of linear combinations of the derivatives of y, then it is known as non-linear ordinary differential equations.

Ordinary Differential Equations Application

ODEs has remarkable applications and it has the ability to predict the world around us. It is used in a variety of disciplines like biology, economics, physics, chemistry and engineering. It helps to predict the exponential growth and decay, population and species growth. Some of the uses of ODEs are:

Modelling the growth of diseases
Describes the movement of electricity
Describes the motion of the pendulum, waves
Used in Newton’s second law of motion and Law of cooling.

Ordinary Differential Equations Examples

Some of the examples of ODEs are as follows;

Ordinary Differential Equations Problems and Solutions

The ordinary differential equations solutions are found in an easy way with the help of integration. Go through once and get the knowledge of how to solve the problem.

👇👇👇👇👇👇👇👇👇👇👇👇👇👇

Question 1:

Find the solution to the ordinary differential equation y’=2x+1

Solution:

Given, y’=2x+1

Now integrate on both sides, ∫ y’dx = ∫ (2x+1)dx

Which gives, y=2x2/2+x+c

y=x2+x+c

Where c is an arbitrary constant.

Question 2:

Solve y4y’+ y’+ x2 + 1 = 0

Solution:

Take, y’ as common,

y'(y4+1)=-x2-1

Now integrate on both sides, we get

y55+y=−x33−x+c

Where c is an arbitrary constant.

For more maths concepts, keep visiting BYJU’S and get various maths related videos to understand the concept in an easy and engaging way.

Imp.Q.

Solve Given that is a solution.

sol.

The given equation can be written in the standard form as

........(1)

Here 1+P+Q=0, therefore is a part of the C.F. of the solution of equation (1).

putting & the corresponding values of in equation (1), we get

or where

or (on integration)

The complete salution of equation (1) is 👈 Ans

Thermal stresses induced in bars of tapering section due to change in temperature_

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Define Temperature Stresses :-

When ever there is some increase or decrease in temperature of a body, it cause the body to expand or contract. If the boys is allowed to expand or contract freely, with the rise or fall of the temperature, no stresses will be induced in the body. But if the deformation of the body is prevented some stresses are induced in the body. Such stresses are called thermal or temperature stresses.
The corresponding strains are called thermal & temperature strain.

Temperature stresses in beams or rods can be calculated as follows -
(i) Determine its expansion or contraction due to change in temperature assuming it is free to expand or contract.
(ii) Calculate the load required to bring the beam in original position.
(iii) Calculate stress and strain corresponding to this load.

l = Original length of the beam
t1 = Initial temperature of the beam
t2 = Final temperature of the beam
= Coefficient of linear expansion of beam material.
(Elongation of the beam due to increase in temperature
If elongation of the beam is prevented by some external force or by fixing its end, temperature strain will produced in beam, which is given by,

and temperature stress

Q. A bar shown in fig. is subjected to axial forces and fixed at L and P. determine the forces in each portion of the bar and displacements of point M and N. Take

n
Sol =>

Given,

Forces in each portion

As we can see from figure, portion LM will be in tension, while portion NP will be in compression.
The free body diagram of all three portion are shown in fig.
Now, for static equilibrium of the bar,

R1+R2=100+50=150kN ........(1)
As bar is fixed at the ends, therefor extension of portion of portion LM will be equal to the compressions of MN & NP i.e,.


    ............(2)

On solving equations (1)&(2), we get

&

Hence, forces in each portion,

      66.67 kN (tensile)





    16.67 kN (compressive)   Ans

& 83.33 kN (compressive )   Ans

Displacement of point M,

0.1587 mm Ans

Displacement of point N,

here

  Displacement of point N,

0.1984 mm Ans

Fourier Transform Question || Engineering mathematics

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FOURIER TRANSFORM:-

The Fourier transform (FT)

decomposes a function of time (a signal) into its constituent frequencies. This is similar to the way a musical chord can be expressed in terms of the volumes and frequencies of its constituent notes. The term Fourier transform refers to both the frequency domain representation and the mathematical operation that associates the frequency domain representation to a function of time.

The Fourier transform of a function of time is itself a complex-valued function of frequency, whose magnitude (modulus) represents the amount of that frequency present in the original function, and whose argument is the phase offset of the basic sinusoid in that frequency. The Fourier transform is not limited to functions of time, but the domain of the original function is commonly referred to as the time domain. There is also an inverse Fourier transform that mathematically synthesizes the original function from its frequency domain representation.

Functions that are localized in the time domain have Fourier transforms that are spread out across the frequency domain and vice versa, a phenomenon known as the uncertainty principle. The critical case for this principle is the Gaussian function, of substantial importance in probability theory and statistics as well as in the study of physical phenomena exhibiting normal distribution (e.g., diffusion). The Fourier transform of a Gaussian function is another Gaussian function. Joseph Fourier introduced the transform in his study of heat transfer, where Gaussian functions appear as solutions of the heat equation.

Definition

The Fourier transform of a function

f

is traditionally denoted

{\hat {f}}

, by adding a circumflex to the symbol of the function. There are several common conventions for defining the Fourier transform of an integrable function

f:\mathbb {R} \to \mathbb {C}

.^[1]^[2] One of them is

{\hat {f}}(\xi )=\int _{-\infty }^{\infty }f(x)\ e^{-2\pi ix\xi }\,dx,

(Eq.1)

for any real number

ξ

A reason for the negative sign in the exponent is that it is common in electrical engineering to represent by

f(x)=e^{2\pi i\xi _{0}x}

a signal with zero initial phase and frequency

\xi _{0}.

^[3]^{[remark 5]} The negative sign convention causes the product

e^{2\pi i\xi _{0}x}e^{-2\pi i\xi x}

to be 1 (frequency zero) when

\xi =\xi _{0},

causing the integral to diverge. The result is a Dirac delta function at

\xi =\xi _{0}

, which is the only frequency component of the sinusoidal signal

e^{2\pi i\xi _{0}x}.

When the independent variable

x

represents time, the transform variable

ξ

represents frequency (e.g. if time is measured in seconds, then frequency is in hertz). Under suitable conditions,

f

is determined by

{\hat {f}}

via the inverse transform:

f(x)=\int _{-\infty }^{\infty }{\hat {f}}(\xi )\ e^{2\pi ix\xi }\,d\xi ,

(Eq.2)

for any real number

x

The statement that

f

can be reconstructed from

{\hat {f}}

is known as the Fourier inversion theorem, and was first introduced in Fourier's Analytical Theory of Heat, although what would be considered a proof by modern standards was not given until much later.The functions

f

and

{\hat {f}}

often are referred to as a Fourier integral pair or Fourier transform pair.

For other common conventions and notations, including using the angular frequency

ω

instead of the frequency

ξ

, see Other conventions and Other notations below. The Fourier transform on Euclidean space is treated separately, in which the variable

x

often represents position and

ξ

momentum. The conventions chosen in this article are those of harmonic analysis, and are characterized as the unique conventions such that the Fourier transform is both unitary on

L 2

and an algebra homomorphism from

L 1

L \infty

, without renormalizing the Lebesgue measure.

Many other characterizations of the Fourier transform exist. For example, one uses the Stone–von Neumann theorem: the Fourier transform is the unique unitary intertwiner for the symplectic and Euclidean Schrödinger representations of the Heisenberg group.

One Questions only important solution:-

Q. Find the fourier transform of pdf

Solidification of metals animation

2019-09-12T12:01:00.000+05:30

Solidification of pure metals take place animation:-

Solidification is the transformation of materials from the liquid the solid crystalline state on cooling.During solidification, the disordered structure of the liquid transforms to the orderly arrangement characteristic of the crystal. This process of solidification does not occur instantaneously. The process is characterized by the formation of numerous small particles of the new phase (s), which increase in size until the transformation completes. The process of solidification may be broken down into two stages-nucleation and grain growth. Nucleation involves the appearance of very small particles called nuclei, these nuclei then grow in size, untill the phase transformation is complete.

solidification of metals animation

All solid metals are crystalline and crystals or grains are made up of several atoms. These individual crystals or grains are aggregated to form a visible mass of solid metal. These grains are formed when liquid metal solidifies. The process of solidification starts when liquid metal cooled below the equilibrium temperature (the temperature at which given metal exist simultaneously solid and liquid phase).
Solidification starts when two or more atoms associate themselves to form very small crystal called nuclei. This may happen simultaneously at a Number of locations throughout the liquid metal. At these points a few atoms assume an orderly arrangement to give the unit cubic structure and growth takes place in three dimensional as shown in fig. As a result of this growth tree like crystals known as dendrites [arise from Greek word dendrom meaning tree ] are formed. A dendrite consists of unit cell, which are exceedingly small, first form in a straight line.

Slow rate of cooling promotes crystallization while a faster cooling rate of cooling rate may prevent crystallization.

Types of SAND in civil Engineering

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Types of sand according to size:-

GREEN SAND

DRY SAND

LOAM SAND

FACING SAND

BACKING SAND

SYSTEM SAND

PARTING SAND

CORE SAND

Define all types SAND:_-

GREEN SAND- It is a mixture of silica sand with 18 to 30 percent clay, having a total water content 6 to 8 percent. The clay and water furnish the bond for green sand. It is fine, soft, light, and porous. Being damp when squeezed in the hand, it retains the shape, the impression given to it under pressure. Moulds prepared in this sand are known as green sand moulds.

DRY SAND- Green sand that has been dried or baked after the mould is made is called dry sand. They are suitable for larger castings. Moulds prepared in this sand are known as dry sand.

LOAM SAND- Loam Sand is high in clay, as much as 50 percent or so, and dries hard. This is particularly employed for laom moulding usually for large castings.

FACING SAND- Facing sand forms the face of the mould. It is used directly next to the surface of the pattern and it comes into contact with the molten metal when the mould is poured. Consequently, it is subjected to the the severest conditions and therefore, must possess, high strength and ls with refractoriness. It is made of silica sand and clay, without the addition of used sand. Different forms of carbon are uscd to prevent the metal from burning into the sand. They are sometimes mixed with 6 to 15 times as much fine moulding sand to make facings.

BACKING SAND- Backing sand or floor sand or floor sand is used to back up the facing sand and to fill the whole volume of the flask. Old, repeatedly used moulding sand is mainly employed for this purpose.
The backing sand is sometimes called black sand because of the fact that old, repeatedly used moulding sand is black in colour due to the addition of coal dust and burning on coming in contact with molten metal.

SYSTEM SAND-In mechanical preparation and handling unit, no facing sand is used. The used sand is cleaned and reactivated by the addition binder in of water binders and special additives. This is known as system sand, In etimes mechanical foundries, where machine moulding is employed so called system sand is used to fill the whole flask. Since the whole mould is made of this system sand therefore, strength, permeability and refractoriness of this sand must be higher than those of backing sand.

PARTING SAND-Parting sand is used to prevent the green sand from sticking to the pattern and also to allow the sand on the parting surface of the cope and drag to separate without clinging. This is clean clay-free silica sand which serves the same purpose as parting dust

CORE SAND- Sand used for making cores is called core sand sometimes called oil sand. This is silica oil sand. This is silica sand mixed with core oil which is composed of linseed oil, resin, light mineral oil and other binding materials. Pitch or flours and water may be used in larger cores for the sake of economy.

Types of SAND in civil Engineering

Stress and strain. Hook's Law

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DEFINE STRESS AND STRAIN:-

Stress-
When some external forces are applied to a body, it offers resistance to these forces. The magnitude of this resisting force is numerically equal to the applied forces. This internal resisting force per unit area is called stress. Therefore, stress can be defined as the intensity of internal forces resisting change in the shape of the body. It is calculated by simply dividing on an area divided by the a: ea. It is measured in N/m2 o: kg the force acting cm2. There are three types of stresses namely, tension, compression and shear. Mathematically,
Stress, a = P/A
where, P= Force applied
A=Cross-sectional area.
[जब कुछ बाहरी बलों को एक निकाय पर लागू किया जाता है, तो यह इन बलों के लिए प्रतिरोध प्रदान करता है। इस प्रतिरोध बल का परिमाण संख्यात्मक रूप से लागू बलों के बराबर होता है। प्रति इकाई क्षेत्र के इस आंतरिक प्रतिरोध बल को तनाव कहा जाता है। इसलिए, तनाव को शरीर के आकार में परिवर्तन का विरोध करने वाली आंतरिक शक्तियों की तीव्रता के रूप में परिभाषित किया जा सकता है। इसकी गणना केवल a: ea द्वारा विभाजित क्षेत्र पर विभाजित करके की जाती है। यह एन / एम 2 ओ में मापा जाता है: बल एक्टिंग सेमी 2 किग्रा। तनाव, संपीड़न और कतरनी जैसे तीन प्रकार के तनाव हैं.]

Types of Stresses;-
The various types of stresses may be classified as follows-

(1) Simple or direct stress
(a) Tension (b) Compression (3) shear

(2) Indirect stress
(a) Bending (2) Torsion

(3) Combined stress

Strain-
Strain is defined as the deformation or change produced in the dimensions of a body due to the effect of stress on it. It is a ratio of the change in dimension to the original dimension. Mathematically

Strain,

where,

Strain is a dimensionless quantity. Depending upon the type of stress, it where, can be of three types, namely tensile, compressive and shearing strain.

Types of Strain ;-
The various types of strains may be classified as follows-

(1) Tensile strain
(2) Compressive strain
(3) Shear strain
(4) Volumetric strain.

Hook's Law;-

Define:

According to Hook's law, when a material is loaded within its elastic limit, the stress is proportional to strain, or in other words, within elastic limits the ratio of stress in a material to the strain produced remains. Mathematical

Where,
E is a constant of proportionality, which is called as a modulus of elasticity, or young's modulus. It has unit as the stress, i. e. or

Poisson's ratio;-
Whenever body is stressed within elastic limits, it is subjected to both longitudinal and lateral deformation. The ratio of the lateral strain to longitudinal strain is a constant quantity for a material and this ratio is known as Poisson's ratio. This ratio is designated by 1/m or u. Mathematically,

Poisson's ratio, 1/m or

Thus,

The limitation of Poisson's ratio is that it can be applied only when material is stressed within the elastic limits

Casting process steps

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CASTING PROCESS

Define ;-(casting)

[ In casting, the molten metal is poured into a refractory mould with a cavity of the shape to be made, and allowed to solidify.After solidification, the desired metal object is taken out from the mould. The solidified object is known as casting. Sand moulds are generally used for casting, however, they cannot maintain better tolerances and smooth surface finish. Thus, now-a- 104days metallic moulds are more common.]

[कास्टिंग में, पिघली हुई धातु को एक आग रोक साँचे में डाला जाता है, जिसे आकार की एक गुहा के साथ बनाया जाता है, और जमने दिया जाता है। जमने के बाद, वांछित धातु की वस्तु को साँचे से बाहर निकाल लिया जाता है। जमना वस्तु कास्टिंग के रूप में जाना जाता है। आम तौर पर कास्टिंग के लिए सैंड मोल्ड का उपयोग किया जाता है, हालांकि, वे बेहतर सहनशीलता और चिकनी सतह खत्म नहीं कर सकते हैं। इस प्रकार, अब- a- 104days धातु के सांचे अधिक आम हैं।]

Various casting processes are as follows-

(i) Sand casting
(ii) Plaster mould casting
(iii) Vacuum casting
(iv) Investment casting
(v) Slush casting
(vi) Pressure casting
(vii) Centrifugal casting
(viii) Continuous casting
(ix) Squeeze casting
(x) Shell mould casting
(xi) Die casting

Applications of Casting-

(i) Automobile parts such as engine blocks, cylinder blocks, pistons, piston rings, etc
(ii) Machine tool structures, e.g. planar beds.
(iii) Wheels and housings of steam and hydraulic turbines, turbine vanes and aircraft jet engine blades.
(iv) Railway crossings (Mn-steel cast section)
(v) Supercharger casing
(vi) Water supply and sewer pipes
(vii) Sanitary fittings
(ix) Agriculture part
(x) Communication,

Define;-(Moulding)

Moulding can be defined as a process of making sound mould of sand by using pattern and cores, so that the metal can be poured into the moulds to produce casting.

MOULDING & CASTING PROCESS_

(I) Expendables mould casting -
In this type of casting processes, the mould cavity is obtained by consolidating a moulding material around a pattern. The commonly used moulding material for these processes is sand or some other refractory material. Because of the sand moulding the dimensions accuracy and surface finish of the casting are not up to the requirements of modern Industries.

NATURAL SEE

(II) Permanent Mould Casting;-
In type of casting processes, the mould is not destroyed after the solidification of the casting and can be used repeatedly. These moulds are adaptable to the production of tens and thousands of castings. The products of this process have smooth surface and better dimensional accuracy. Due to the high cost of permanent moulds their use is limited to mass production of small and medium sized parts of light non- ferrous alloys

(iii) Semi-permanent Mould Casting;-
In this type of casting processes, moulds are prepared from high refractory materials like graphite These moulds are less durable as compared to permanent moulds and can only be used for few tens of castings.

Properties of sand in construction

(1) Porosity
(2) Flowability
(3) Collapsibility
(4) Adhesiveness
(5) Cohesiveness or Strength
(6) Refractoriness
(7) Chemical Resistivity

casting process download pdf

Fourier Transform

2019-09-04T23:51:00.002+05:30

The Fourier Transform

1.1 Fourier transforms as integrals
There are several ways to define the Fourier transform of a function f : R → C. In this section, we define it using an integral representation and state some basic uniqueness and inversion properties, without proof. Thereafter, we will consider the transform as being defined as a suitable limit of Fourier series, and will prove the results stated here.

The Fourier Transform is one of deepest insights ever made. Unfortunately, the meaning is buried within dense equations:

Yikes. Rather than jumping into the symbols, let's experience the key idea firsthand. Here's a plain-English metaphor:

What does the Fourier Transform do? _Given a smoothie, it finds the recipe.
How? _Run the smoothie through filters to extract each ingredient.
Why? _Recipes are easier to analyze, compare, and modify than the smoothie itself.
How do we get the smoothie back? _Blend the ingredients.

Here's the "math English" version of the above:The Fourier Transform takes a time-based pattern, measures every possible cycle, and returns the overall "cycle recipe" (the amplitude, offset, & rotation speed for every cycle that was found).

Time for the equations? No! _Let's get our hands dirty and experience how any pattern can be built with cycles, with live simulations.

If all goes well, we'll have an aha!_moment and intuitively realize why the Fourier Transform is possible. We'll save the detailed math analysis for the follow-up.

This isn't a force-march through the equations, it's the casual stroll I wish I had. Onward!

function
Fourier transform--1	1
Fourier transform--cosine
Fourier transform--delta function
Fourier transform--exponential function
Fourier transform--Gaussian
Fourier transform--Heaviside step function
Fourier transform--inverse function
Fourier transform--Lorentzian function
Fourier transform--ramp function
Fourier transform--sine

Fourier transform formula PDF

Laws of Thermodynamics Equilibrium

2019-09-02T01:00:00.002+05:30

THERMODYNAMIC EQUILIBRIUM (थायरोडायनामिक एक्विलिब्रियम)

Equilibrium Expressions

Equilibrium Constant Expressions	Rules for Writing Equilibrium Constant Expressions	Altering or Combining Equilibrium Reactions
Reaction Quotients: A Way to Decide Whether a Reaction is at Equilibrium	Changes in Concentration that Occur as a Reaction Comes to Equilibrium	Hidden Assumptions that Make Equilibrium Calculations Easier
A Rule of Thumb for Testing the Validity of Assumptions	What Do We Do When the Approximation Fails?	Equilibria Expressed in Partial Pressures
The Effect of Temperature on a Chemical Reaction

A system is said to exist in a state of thermodynamic equilibrium when no change in any macroscopic property is registered, if the system is isolated from its surroundings

An isolated system always reaches in course of time a state of thermodynamic equilibrium and can never depart from it spontaneously .
Therefore, there can be no spontaneous change in any macroscopic property if the system exists in an properties of physical systems that are found in equilibrium states .
A system will be in a state of thermodynamic equilibrium, if the conditions for the following three types of equilibrium are satisfied:

(a) Mechanical equilibrium
(b) Chemical equilibrium
(c) Thermal equilibrium

(ए) मैकेनिकल संतुलन

(b) रासायनिक संतुलन

(c) थर्मल संतुलन

In the absence of any unbalanced force within the system itself and also between the system and the surroundings, the system is said to be in a state of mechanical equilibrium. If an unbalanced force exists, either the system alone or both the system and the surroundings will undergo a change of state till mechanical equilibrium is attained.
👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇
(सिस्टम के भीतर और सिस्टम और परिवेश के बीच किसी भी असंतुलित बल की अनुपस्थिति में, सिस्टम को यांत्रिक संतुलन की स्थिति में कहा जाता है। यदि कोई असंतुलित बल मौजूद है, तो या तो प्रणाली या दोनों प्रणाली और परिवेश यांत्रिक संतुलन प्राप्त होने तक राज्य के परिवर्तन से गुजरेंगे।)

If there is no chemical reaction or transfer of matter from one part of the system to another, such as diffusion or solution, the system is said to exist in a state of chemical equilibrium equilibrium state. Thermodynamics studies mainly the

When a system existing in mechanical and chemical equilibrium is separated from its surroundings by a diathermic wall (diathermic means 'which allows heat to flow') and if there is no spontaneous change in any property of the system, the system is said to exist in a state of thermal equilibrium. When this is not satisfied, the system will undergo a change of state till thermal equilibrium is restored
When the conditions for any one of the three types of equilibrium are not satisfied, a system is said to be in a nonequilibrium state. If the nonequilibrium of the is due to an unbalanced force in the interior of a system or between the system and the surroundings, the pressure varies from one part of the system to another. There is no single pressure that refers to the system as a whole. Similarly if the nonequilibrium is because of the temperature of the system being different from that of its surroundings, there is a nonuniform temperature distribution set up within the system and there is no single temperature that stands for the system as a whole. It can thus be inferred that when the conditions for thermodynamic equilibrium are not satisfied, the states passed through by a system cannot be described by thermodynamic properties which represent the system as a whole.
Thermodynamic properties are the macroscopic coordinates defined for, and significant to, only thermodynamic equilibrium states. Both classical and statistical thermodynamics study mainly the equilibrium states of a system.
(थर्मोडायनामिक गुण स्थैतिक निर्देशांक हैं, और केवल थर्मोडायनामिक संतुलन राज्यों के लिए महत्वपूर्ण हैं। शास्त्रीय और सांख्यिकीय दोनों थर्मोडायनामिक्स मुख्य रूप से एक प्रणाली के संतुलन राज्यों का अध्ययन करते हैं।)

In a balanced chemical equation, the total number of atoms of each element present is the same on both sides of the equation. Stoichiometric coefficients are the coefficients required to balance a chemical equation. These are important because they relate the amounts of reactants used and products formed. The coefficients relate to the equilibrium constants because they are used to calculate them. For this reason, it is important to understand how to balance an equation before using the equation to calculate equilibrium constants.

Introduction

There are several important rules for balancing an equation:

An equation can be balanced only by adjusting the coefficients.
The equation must include only the reactants and products that participate in the reaction.
Never change the equation in order to balance it.
If an element occurs in only one compound on each side of the equation, try balancing this element first.
When one element exists as a free element, balance this element last.

Example

1

H_{2} (g) + O_{2} (g) ⇌ H_{2} O (l)

Because both reactants are in their elemental forms, they can be balanced in either order. Consider oxygen first. There are two atoms on the left and one on the right. Multiply the right by 2	$H_{2} (g) + O_{2} (g) ⇌ 2 H_{2} O (l)$
Next, balance hydrogen. There are 4 atoms on the right, and only 2 atoms on the left. Multiply the hydrogen on left by 2	$2 H_{2} (g) + O_{2} (g) ⇌ 2 H_{2} O (l)$
Check the stoichiometry. Hydrogen: on the left, 2 x 2 = 4; on right 2 x 2= 4. Oxygen: on the left: 1 x 2 = 2; on the right 2 x 1 = 2 . All atoms balance, so the equation is properly balanced.	$2 H_{2} (g) + O_{2} (g) ⇌ 2 H_{2} O (l)$

Example

2

A l (s) + M n S O_{4} (a q) ⇌ A l_{2} (S O_{4})_{3} + M n; (s)

First, consider the SO42- ions. There is one on the left side of the equation, and three on the right side. Add a coefficient of three to the left side.	$A l (s) + 3 M n S O_{4} (a q) ⇌ A l_{2} (S O_{4})_{3} + M n (s)$
Next, check the Mn atoms. There is one on the right side, but now there are three on the left side from the previous adjustment. Add a coefficient of three on the right side.	$A l (s) + 3 M n S O_{4} (a q) ⇌ A l_{2} (S O_{4})_{3} + 3 M n (s)$
Consider Al. There is one atom on the left side and two on the right side. Add a coefficient of two on the left side. Make sure there are equal numbers of each atom on each side.	$2 A l (s) + 3 M n S O_{4} (a q) ⇌ A l_{2} (S O_{4})_{3} + 3 M n (s)$

Homogeneous system in thermodynamics

2019-09-01T17:52:00.001+05:30

Homogeneous system in thermodynamics

https://surmilam.blogspot.com/

A quantity of matter homogeneous throughout in chemical compound and physically structure is called a phase. Every substance can exits change in any one of the three phases, viz. Solid, liquid and gas. A system consisting of a signal phase is called a homogeneous system, while a system consisting of more than one phase is known as a heterogeneous system.

(रासायनिक यौगिक और भौतिक संरचना में पूरे मामले में सजातीय मात्रा को एक चरण कहा जाता है। प्रत्येक पदार्थ तीन चरणों में से किसी एक में परिवर्तन से बाहर निकल सकता है, अर्थात। ठोस, तरल और गैस। सिग्नल चरण वाली प्रणाली को एक सजातीय प्रणाली कहा जाता है, जबकि एक से अधिक चरण वाली प्रणाली को विषम प्रणाली के रूप में जाना जाता है।)

(पदार्थ अलग-अलग चरणों में अलग-अलग दबावों और तापमानों पर दिखाई देता है। उदाहरण के लिए, सामान्य तापमान पर पानी तरल रूप में होता है। यदि तापमान बढ़ा है तो यह गैसीय रूप में बदल जाता है। दबाव कम होने पर पानी वाष्प में भी बदल जाता है। यदि तापमान ℃ से कम हो जाता है तो पानी ठोस बर्फ बन जाता है। तो, पानी 3 चरणों में मौजूद है, ठोस, तरल और गैस।)

Homogeneous system:

The system that has single or uniform phase such as like solid or liquid or gaseous is called as homogeneous system.

Heterogeneous system:
The system that has more than one phase i.e. the combination of solid, liquid and gaseous state is called as heterogeneous system.

(सजातीय प्रणाली:
वह व्यवस्था जिसमें एकल या एक समान चरण होते हैं जैसे ठोस या तरल या गैसीय को सजातीय प्रणाली कहा जाता है।

विषम प्रणाली:
वह प्रणाली जिसमें एक से अधिक चरण होते हैं यानी ठोस, तरल और गैसीय अवस्था के संयोजन को विषम प्रणाली कहा जाता है।)

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A homogeneous thermodynamic system is defined as the one whose chemical composition and physical properties are the same in all parts of the system, or change continuously from one point to another. A homogeneous system can be exemplified by imagining a column of atmospheric air, which is a mixture of a number of gases, mainly nitrogen and oxygen. In a system of this kind, acted upon by the force of gravity, both the composition of the system and its physical properties will continuously change from one point to another.

(एक सजातीय थर्मोडायनामिक प्रणाली को उसी के रूप में परिभाषित किया गया है जिसकी रासायनिक संरचना और भौतिक गुण प्रणाली के सभी भागों में समान हैं, या एक बिंदु से दूसरे तक लगातार बदलते रहते हैं। एक सजातीय प्रणाली को वायुमंडलीय हवा के एक स्तंभ की कल्पना करके अनुकरण किया जा सकता है, जो कई गैसों का मिश्रण है, मुख्य रूप से नाइट्रोजन और ऑक्सीजन। इस तरह की प्रणाली में, गुरुत्वाकर्षण बल द्वारा कार्य किया जाता है, सिस्टम की संरचना और इसके भौतिक गुण दोनों एक बिंदु से दूसरे बिंदु तक लगातार बदलते रहेंगे।)

A heterogeneous system is denned as one consisting of two or more homogeneous bodies. The homogeneous bodies of a heterogeneous system are referred to as phases. Each phase is separated from other phases by interfaces, or boundaries, and in passing over such a boundary the chemical composition of the substance or its physical properties abruptly change. This phase boundary must not be regarded as a mathematical surface but as a thin layer separating the phases, a layer where the properties of one phase pass, or turn, rapidly into the properties of the other phase.

(एक विषम प्रणाली को दो या अधिक सजातीय निकायों से मिलकर बनाया जाता है। एक विषम प्रणाली के सजातीय निकायों को चरणों के रूप में संदर्भित किया जाता है। प्रत्येक चरण को अन्य चरणों से अलग किया जाता है इंटरफेस, या सीमाओं द्वारा, और इस तरह की सीमा पर पदार्थ या उसके भौतिक गुणों के रासायनिक संरचना में अचानक परिवर्तन से गुजरता है। इस चरण की सीमा को गणितीय सतह के रूप में नहीं, बल्कि चरणों को अलग करने वाली एक पतली परत के रूप में माना जाना चाहिए, एक परत जहां एक चरण के गुण पास होते हैं, या दूसरे चरण के गुणों में तेजी से बदलते हैं।)

Example;

An example of a heterogeneous system is water with ice floating in it. This system has two homogeneous bodies, water and ice. The chemical composition of the two phases is the same, but their physical properties differ drastically.

Another example of a heterogeneous system is the content of a sealed steel tube containing liquid mercury, liquid ethyl alcohol, and a mixture of saturated vapors of the alcohol and mercury. This heterogeneous system comprises three phases. The first phase is the liquid mercury, the second is the liquid ethyl alcohol, and the third phase is represented by the mixture of saturated vapors. Here the chemical compositions and the physical properties of all phases are different.

A homogeneous system and each phase of a heterogeneous system may consist of one or several pure substances.

A homogeneous system or the phase of a heterogeneous system that consist of several pure substances is called a solution or mixture.

All pure substances and solutions can exist in three states of aggregation: gas, liquid and solid.

Thermodynamics system wikipedia

List for thermodynamic system of properties

2019-08-28T00:57:00.000+05:30

List of thermodynamic properties ;_ 5)

1) Thermodynamics System 1) थर्मोडायनामिक्स सिस्टम

2) Thermodynamics Equilibrium 2) ऊष्मप्रवैगिकी संतुलन

3) Thermodynamics State 3) ऊष्मप्रवैगिकी राज्य

4) Thermodynamics Property 4) ऊष्मप्रवैगिकी संपत्ति

5) Thermodynamics Process 5) ऊष्मप्रवैगिकी प्रक्रिया

Point Function;_( बिंदु फलन )

A Point function (also known as state function) is a function whose value depends on the final and initial states of the thermodynamic process, irrespective of the path followed by the process.

Example of point functions are density, enthalpy, internal energy, entropy etc.

P- presser दाब

V- volume आयतन

T- temperature ताप

S- enthalpy

N- entropy

U- Internal energy

Difference between point function and path function ;- 8)

Sr. no.	Point Function	Path Function
1	Its values are based on the state of the system (i.e. pressure, volume, temperature etc.)	Its values are based on how that particular thermodynamic state is achieved.
2	No matter by which process the state is obtained, its values will always remain the same.	Different processes to obtain a particular state will give us different values.
3	Only initial and final states of the process are sufficient	We need to know exact path followed by the process
4	Its values are independent of the path followed	Its values are dependent on the path followed
5	It is an exact or perfect differential	It is an inexact or imperfect differential.
6	Its cyclic integral is always zero	Its cyclic integral may or may not be zero
7	It is property of the system	It is not the property of the system
8	Its examples are density, enthalpy, internal energy, entropy etc	Its examples are Heat, work etc.

THERMODYNAMIC PROPERTIES ,PROCESSES & CYCLES

Every system has certain characteristics by which its physics condition may be describe, e.g volume, temperature, pressure, etc. Such characteristics are called properties of the system. These are all microscopy in nature. When all the properties of a system have definite Values, the system is said to exist at a definite state. Properties are the coordinates to describe the state of a system. They are the state variable of the system. Any operation in which one or more of the properties of a system change is called a change of state. The succession of states passed through during a change of state is called the path of the change of state. When the path is completely specified, the change of state is called a processes, e.g. a constant pressure process.

A thermodynamic cycle is defined as a series of state change such that the final state is identical which the initial state.

A process and a cycle process

Properties may be of two types. Intensive properties are independent of the mass in the system, e.g. pressure, temperature, etc. Extensive properties also increase. Specific extensive properties, i.e. extensive properties per unit mass, are intensive properties, e.g. specific volume, specific energy, etc.

Relationship of thermodynamics

2019-08-25T23:42:00.001+05:30

Relationship between heat work and temperature heat is a from energy. It is always flowing from higher temperature to lower temperature it can not flow from lower temperature to higher temperature it is not the properties of the system ,property of their temperature.

(गर्मी के काम और तापमान गर्मी के बीच संबंध ऊर्जा से है। यह हमेशा उच्च तापमान से निचले तापमान तक बहता है यह निम्न तापमान से उच्च तापमान तक नहीं बह सकता है यह सिस्टम के गुण नहीं हैं, उनके तापमान की संपत्ति।)

What is this thermodynamics ? ऊष्मप्रवैगिकी :

2019-08-25T21:58:00.003+05:30

Thermodynamics

Thermodynamics as branch of science in which study of heat energy to other from of energy or vice-versa. that is called as Thermodynamic.

Thermodynamics system;

It is part in the space on which attention fours for study, that is called as thermodynamics system.

Surrounding;

Every things out side the system that is called as surrounding.

Boundary ;

Not interaction which system and surrounding or separation, part's that is called as boundary.