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)?

Step-by-step solution

The ideal gas equation for n moles is PV = nRT . Given the process equation P = kT , where k is a constant. Substituting P into the ideal gas equation, we get: (kT)V = nRT V = nR k Since n , R , and k are constants, the volume V is constant. Thus, the process is isochoric. For an isochoric process, the work done dW = P dV = 0 . From the first law of thermodynamics, dQ = dU + dW = dU . Since dU = nC_V dT and dQ = nC dT , we have: nC dT = nC_V dT C = C_V Answer: C = C_V