For an ideal gas, a process is described by P = kT, where k is a constant. If the molar heat capacity for this process is C, then which one of the following is correct (where the symbols have their usual meanings)?
- A. C = C_P
- B. C = C_V ✓
- C. C = (C_P + C_V) / 2
- D. C \text{ is never constant}
Correct Answer: B. C = C_V
Explanation
From the ideal gas equation PV = RT (for 1 mole) and the given process P = kT, we have kTV = RT, which implies V = \frac{R}{k} = \text{constant}. Since volume is constant, it is an isochoric process and C = C_V.
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