Question

\(C_p\), the heat capacity at constant pressure is given by:

• A. \(\left( \frac{\partial H}{\partial T} \right)_P\)
• B. \(\left( \frac{\partial E}{\partial T} \right)_P\)
• C. \(\left( \frac{\partial A}{\partial T} \right)_P\)
• D. \(\left( \frac{\partial G}{\partial T} \right)_P\)

Hint:

Always associate \(C_p\) with enthalpy \(H\) and \(C_v\) with internal energy \(E\). Use partial derivatives with respect to temperature.

Answer 1

The Correct Option is A

The heat capacity at constant pressure, \(C_p\), is defined as the amount of heat required to raise the temperature of a substance by one degree at constant pressure.
In thermodynamics, it is related to the change in enthalpy \(H\) with respect to temperature \(T\), at constant pressure: \[ C_p = \left( \frac{\partial H}{\partial T} \right)_P \] This is because at constant pressure, the heat added to the system goes into increasing the enthalpy.
The other expressions involve internal energy \(E\), Helmholtz free energy \(A\), and Gibbs free energy \(G\), none of which directly represent \(C_p\) under constant pressure.