A mono-atomic gas `X` and an diatomic gas `gamma` both initially at the same temperature and pressure are compressed adiabatically from a volume `V` to `V//2`. Which gas will be at higher temperature?

Options

A. `X`
B. `Y`
C. both are same
D. Cannot be determined

Explanation

To solve the problem of determining which gas will be at a higher temperature after undergoing adiabatic compression, we can follow these steps:

### Step 1: Understand the Adiabatic Process
In an adiabatic process, there is no heat exchange with the surroundings. The relationship between temperature and volume for an ideal gas undergoing an adiabatic process can be expressed as:
\[ T_1 V^{\gamma - 1} = T_2 V^{\gamma - 1} \]
Where:
- \( T_1 \) is the initial temperature,
- \( T_2 \) is the final temperature,
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