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, the state equation is PV = nRT. The given process is described by the equation P = kT, where k is a constant. By substituting the expression for pressure P = nRT/V into the process equation, we get:
nRT/V = kT
Dividing both sides by T (where T ≠ 0), we obtain:
nR/V = k
Rearranging for volume: V = nR/k. Since n, R, and k are all constants, the volume V remains constant throughout the process. This identifies the process as an isochoric process. By definition, the molar heat capacity for any process occurring at constant volume is Cv. Therefore, for this specific process, C = Cv.