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)?

For an ideal gas, PV = nRT. Given P = kT, dividing by T gives P/T = k, so V = nR/k = constant. Wait — substituting P = kT into PV = nRT gives kTV = nRT, so V = nR/k = constant. This means the process is isochoric (constant volume), which would give C = C_V. However, re-examining: if P = kT and PV = nRT, then V = nR/k (constant), so volume is constant. Actually, let's reconsider — if V is constant the process is isochoric and C = C_V. But the standard answer for this type of problem with P proportional to T at constant V indicates this is isochoric. Reviewing once more carefully: from P = kT and PV = nRT, we get V = nR/k = constant, indicating isochoric process where C = C_V. Hence the correct heat capacity is C_V.