One mole of oxygen being initially at a temperature `T_0 = 290 K` is adiabatically compressed to increase its pressure `eta = 10.0` times. Find :
(a) the gas temperature after the compression ,
(b) the work that has been performed on the gas.

Explanation

To solve the problem step by step, we will follow the principles of thermodynamics, specifically focusing on the adiabatic process for an ideal gas.

### Given:
- Initial temperature, \( T_0 = 290 \, \text{K} \)
- Pressure increase factor, \( \eta = 10.0 \) (i.e., \( P_2 = 10 P_1 \))
- Number of moles, \( n = 1 \) (for oxygen)
- For diatomic gases like oxygen, the adiabatic index \( \gamma \approx 1.4 \)

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