A sample of an ideal gas in a cyclinder is compressed adiabatically to `1/3rd` of its volume. Will final pressure be more or less than `3 times` the initial pressure?

Explanation

To solve the problem, we will use the adiabatic process equation for an ideal gas, which states that \( PV^\gamma = \text{constant} \), where \( \gamma \) (gamma) is the heat capacity ratio (specific heat at constant pressure divided by specific heat at constant volume).

### Step-by-Step Solution:

1. **Understanding the Adiabatic Process**:
- In an adiabatic process, there is no heat exchange with the surroundings. The relationship between pressure and volume for an ideal gas is given by the equation:
\[
P_i V_i^\gamma = P_f V_f^\gamma
...