What is a polytropic process, Obtain expressions for work done in a polytropic process and specific heat of gas in such a process.

Explanation

### Step-by-Step Solution

#### Step 1: Definition of Polytropic Process
A polytropic process is defined as a thermodynamic process in which the pressure \( P \) multiplied by the volume \( V \) raised to the power of \( \alpha \) remains constant. Mathematically, this can be expressed as:
\[ PV^\alpha = \text{constant} \]
Different values of \( \alpha \) correspond to different thermodynamic processes:
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