I am trying to derive certain formulas and and I feel like the following expression is good for my derivation. (du/dT)_p=(dU/dT)_V I am trying to say that the above expression is true because of first law of thermodynamics. any suggestions weather if this approach is good or not

teevaituinomakw

teevaituinomakw

Answered question

2022-09-03

I am trying to derive certain formulas and and I feel like the following expression is good for my derivation.
( u T ) p = ( u T ) V
I am trying to say that the above expression is true because of first law of thermodynamics. any suggestions weather if this approach is good or not

Answer & Explanation

adwelirlz

adwelirlz

Beginner2022-09-04Added 10 answers

d U = ( U T ) V d T + ( U V ) T d V
d V = ( V T ) P d T + ( V P ) T d P
so
d U = [ ( U T ) V + ( U V ) T ( V T ) P ] d T + ( U V ) T ( V P ) T d P
So,
( U T ) P = [ ( U T ) V + ( U V ) T ( V T ) P ]
According to this, your equation is correct for an ideal gas, but not for a real gas beyond the ideal gas region.

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