An ideal gas is made to undergo a process `T = T_(0)e^(alpha V)` where `T_(0)` and `alpha` are constants. Find the molar specific heat capacity of the gas in the process if its molar specific heat capacity at constant volume is `C_(v)`. Express your answer as a function of volume (V).

Explanation

To find the molar specific heat capacity of an ideal gas undergoing the process \( T = T_0 e^{\alpha V} \), we will follow these steps:

### Step 1: Use the First Law of Thermodynamics
The first law of thermodynamics states:
\[ dq = dU + dW \]
where \( dq \) is the heat added to the system, \( dU \) is the change in internal energy, and \( dW \) is the work done by the system.
...