A monoatomic gas is compressed adiabatically to `(8)/(27)` of its initial volume if initial temperature is `27^@C`, find increase in temperature

Explanation

To solve the problem of finding the increase in temperature of a monoatomic gas that is compressed adiabatically to \( \frac{8}{27} \) of its initial volume, we can follow these steps:

### Step 1: Understand the Given Information
- Initial temperature \( T_1 = 27^\circ C = 300 \, K \) (converted to Kelvin)
- Initial volume \( V_1 = V_0 \)
- Final volume \( V_2 = \frac{8}{27} V_0 \)
- The gas is monoatomic, so \( \gamma = \frac{5}{3} \).

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