A) State a version of the Third Law of Thermodynamics. b) By...

a) State a version of the Third Law of Thermodynamics. b) By considering S(T, V), show that: ?S = ? (cV/T) dT + ? (dP/dT)v dV. c) Calculate an expression for the change in entropy when one mole of a monoatomic ideal gas is heated from T0 to T at constant pressure. d) For an ideal gas at constant pressure, sketch the dependence of entropy on temperature. e) Discuss the behaviour of the entropy of an ideal gas as T ? 0. What can one conclude about the ideal gas equations in this limit?

Transcript

00:03 Basically, temperature signifies the average energy of the particle in any body.

00:12 For example, let's suppose there is a liquid and it has got particles or otherwise there is a solid at least, say, at temperature 20 degrees celsius.

00:27 So the temperature of this object basically tells about the average.

00:32 Average energy carrying by the constituent particles of this body.

00:42 So when the temperature of this material goes almost to 0 kelvin, that reaches at a 0 kelvin near about, because theoretically it is impossible to reach any object's temperature at a 0 kelvin.

01:00 So let's say it is 0 .12 kelvin or something like 0 .5 kelvin, which is still much, much lower temperature.

01:10 Then this average movement of this constituent atoms or the molecules becomes 0.

01:23 That is, they become a perfect crystalline object where the all of the all.

01:31 Modes of motion that is their average vibration from their mean position, average rotation and translation, this all becomes zero.

01:45 So we can also say that this means that the entropy of the system reaches zero.

01:52 So third law of thermodynamics basically tells that when temperature reaches to near about 0 kelvin, the entropy of the system or entropy of the object also becomes 0.

02:06 So this is the third law of thermodynamics.

02:09 Now coming to the second question, let's suppose entropy as is the function of temperature t and b, that is the entropy of any system or object depends upon the variable or the property, temperature, and volume.

02:32 So we can write that s is the function of temperature t and v.

02:38 So upon differentiation or taking a very small change in entropy, let's say delta s, we can write del s by del t at constant v into dt plus del s by del s by del v at constant t into d v basically this term says that if it put the volume constant and change the temperature with with a very within very small limit the amount of the change in entropy will be represented by this term that is here v is that is volume is constant.

03:32 Now similarly in the second term the temperature is taken constant and change in entropy is analyzed or taken with respect to change in the volume.

03:48 Now multiplying both sides by temperature t we can write t ds or t into delta s that can be written as tds is equals to t into del s by del t at constant v into d t plus t into del s by del v at constant t into d v...

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