An ideal gas is taken through a process in which the pressure and the volume are changed according to the equation `p=kv`. Show that the molar heat capacity of the gas for the process is given by `(C=C_v + ( R)/(2))`.

Explanation

To solve the problem of finding the molar heat capacity \( C \) of an ideal gas undergoing a process defined by the equation \( p = kV \), we will follow these steps:

### Step 1: Use the Ideal Gas Equation
We start with the ideal gas equation:
\[ pV = nRT \]
Substituting \( p = kV \) into the ideal gas equation gives:
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