For an ideal gas, a process is described by P = kT , where k is a...

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:

$(kT)V = nRT$

$V = \dfrac{nR}{k}$

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: $C = C_V$