A container having slightly conducting walls contains air. The initial temperature and volume are `47^(@)C` (equal to the temperature of the surrounding) and `400cm^(3)` respectively. Find the rise in the temperature if the gas is compressed to `200cm^(3)` (a) in a short time (b) in a short time (b) in a along time. Take `gamma = 1.4. [2^(0.4) = 1.3]`

Explanation

To solve the problem, we will analyze the two scenarios: (a) when the gas is compressed in a short time (adiabatic process) and (b) when the gas is compressed in a long time (isothermal process).

### Given Data:
- Initial Temperature, \( T_i = 47^\circ C = 47 + 273 = 320 \, K \)
- Initial Volume, \( V_i = 400 \, cm^3 \)
- Final Volume, \( V_f = 200 \, cm^3 \)
- \( \gamma = 1.4 \)

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