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Question

Physics Question on Thermodynamics

For a thermodynamic system, the coefficient of volume expansion β=1V(VT)P\beta=\frac{1}{V}(\frac{∂V}{∂T})_P and compressibility K=1V(VP)TK=-\frac{1}{V}(\frac{∂V}{∂P})_T , where V, T, and P are respectively the volume, temperature, and pressure. Considering that dVV\frac{dV}{V} is a perfect differential, we get

A

(βP)T=(KT)P(\frac{∂\beta}{∂P})_T=(\frac{∂K}{∂T})_P

B

(βT)P=(KP)T(\frac{∂\beta}{∂T})_P=-(\frac{∂K}{∂P})_T

C

(βP)T=(KT)P(\frac{∂\beta}{∂P})_T=-(\frac{∂K}{∂T})_P

D

(βT)P=(KP)T(\frac{∂\beta}{∂T})_P=(\frac{∂K}{∂P})_T

Answer

(βP)T=(KT)P(\frac{∂\beta}{∂P})_T=-(\frac{∂K}{∂T})_P

Explanation

Solution

The correct option is (C) : (βP)T=(KT)P(\frac{∂\beta}{∂P})_T=-(\frac{∂K}{∂T})_P.