Question

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

• A. \((\frac{∂\beta}{∂P})_T=(\frac{∂K}{∂T})_P\)
• B. \((\frac{∂\beta}{∂T})_P=-(\frac{∂K}{∂P})_T\)
• C. \((\frac{∂\beta}{∂P})_T=-(\frac{∂K}{∂T})_P\)
• D. \((\frac{∂\beta}{∂T})_P=(\frac{∂K}{∂P})_T\)

Answer 1

The Correct Option is C

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