Suppose 1.00 L of a gas with `gamma`= 1.30, initially at 285 K and 1.00 atm, is suddenly compressed adiabatically to half its initial volume. Find its final (a) pressure and (b) temperature. (C) If the gas is then cooled to 273 K at constant pressure, what is its final volume?

Explanation

To solve the problem step by step, we will use the principles of thermodynamics, specifically the first law of thermodynamics and the equations governing adiabatic processes.

### Given Data:
- Initial Volume, \( V_A = 1.00 \, \text{L} \)
- Final Volume after compression, \( V_B = \frac{V_A}{2} = 0.50 \, \text{L} \)
- Initial Temperature, \( T_A = 285 \, \text{K} \)
- Initial Pressure, \( P_A = 1.00 \, \text{atm} \)
- Adiabatic index, \( \gamma = 1.30 \)
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