Two gases have the same initial pressure P, volume V and temperature T. They both expand to the same volume from V to 2V, one adiabatically and the other isothermally. Plot P-V diagram for the given situation and hence explain. In which case is the final temperature greater?

Explanation

To solve the problem, we will analyze the expansion of two gases—one undergoing adiabatic expansion and the other undergoing isothermal expansion. We will plot the P-V diagram for both processes and determine which case results in a higher final temperature.

### Step-by-Step Solution:

1. **Initial Conditions**:
- Both gases have the same initial conditions: pressure \( P \), volume \( V \), and temperature \( T \).

2. **Final Volume**:
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