Question

If 
\(v\) is the mass specific volume,
\(s\) is the mass specific entropy,
\(P\) is the pressure,
\(T\) is the temperature, 
then using Maxwell relations, \[ \left( \frac{\partial s}{\partial P} \right)_T = \]

• A. \( \left( \frac{\partial v}{\partial T} \right)_P \)
• B. \( - \left( \frac{\partial v}{\partial T} \right)_P \)
• C. \( \left( \frac{\partial v}{\partial T} \right)_S \)
• D. \( - \left( \frac{\partial v}{\partial T} \right)_S \)

Hint:

The Maxwell relations allow us to express the partial derivatives of thermodynamic variables in terms of each other, aiding in simplifying thermodynamic calculations.

Answer 1

The Correct Option is B

Maxwell relations are derived from the fundamental thermodynamic equations. The given problem uses the Maxwell relation that relates the change in entropy with respect to pressure at constant temperature. This is derived from the thermodynamic potentials and can be obtained from the following relation: \[ \left( \frac{\partial s}{\partial P} \right)_T = - \left( \frac{\partial v}{\partial T} \right)_P. \] Hence, the correct answer is \( (B) - \left( \frac{\partial v}{\partial T} \right)_P \). Final Answer: (B) \( - \left( \frac{\partial v}{\partial T} \right)_P \)