The specific heat at constant pressure of a real gas obeying P V²=R T equation is:

Solution

Physics sir · 3 steps

Hold P fixed, differentiate PV² = RT to get dV/dT, and the work term gives you the extra bit.

1. First law, constant P. For one mole heated at constant pressure, dQ = dU + P dV. Take dU = C_V dT, the usual assumption, so C_P = dQ/dT = C_V + PdV/dT.
2. Differentiate the equation. With P constant, differentiating PV² = RT gives 2PV dV = R dT. So dV/dT = R/2PV.

   PdV/dT = P × R/2PV = R/2V

3. So. C_P = C_V + R/2V, which is option (c).

The idea to keep. For any equation of state, C_P - C_V = P((∂ V)/(∂ T))_P when U depends only on T. Differentiate the given equation at constant P and you are done.

Answer from the NTA final answer key. Solution by PrepWiser.