00:01
Hi, in this question we need to find the relation for do yes by do v keeping t constant do s by do v keeping the temperature constant for an ideal gas using maxwell's relation and ideal gas equation of state.
00:20
The helmolds function or the helmolds free energy can be written as f is equal to u minus t now you is the internal energy, t is the temperature and s is the entropy.
00:41
Let this be our equation number 1.
00:45
Differently in this equation we get df is equal to d .u minus tds minus s d t dt.
01:03
Here this d u, this d u that is the change in internal energy can be written as a tds pds minus pdv.
01:19
Now this d .f becomes f is equal to minus pdv minus s dt.
01:35
Let this be our equation number two.
01:41
Differentiating this equation partially with respect to the volume and the temperature we get do yf by do b keeping the temperature constant is equal to minus p and another equation do f by do t keeping the volume constant will yield minus s let this be our equation number 3.
02:23
Since the d .f is a perfect differential, we can write do by do v, do v, do v, do f by do t is equal to do by do t, do by do t, now from the equation number 3, we can write do s by doe v keeping constant, keeping temperature constant...
