A gas is enclosed in a cylindrical can fitted with a piston. The walls of the can and the piston are adiabatic. The initial pressure , volume and temperature of the gas are `100 kPa, 400cm^(3)` and `300K` respectively. The ratio of the specific heat capacities of the gas is `(C_p / C_v = 1.5)` Find the pressure and the temperature of the gas if it is (a) suddenly compressed (b) slowly compressed to `100 cm^(3)`.

Explanation

To solve the problem, we need to analyze the adiabatic process of the gas when it is compressed. Given the initial conditions and the specific heat capacity ratio, we can find the final pressure and temperature after compression.

### Step-by-Step Solution:

1. **Identify Initial Conditions:**
- Initial Pressure, \( P_1 = 100 \, \text{kPa} \)
- Initial Volume, \( V_1 = 400 \, \text{cm}^3 \)
- Initial Temperature, \( T_1 = 300 \, \text{K} \)
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