`2m^(3)` volume of a gas at a pressure of `4xx10^(5) Nm^(-2)` is compressed adiabatically so that its volume becomes `0.5m^(3)` Find the new pressure . Compare this with the pressure that would result if the compression was isothermal. Calculate work done in each `gamma = 1.4`

Explanation

To solve the problem, we will follow these steps:

### Step 1: Identify the given values
- Initial volume, \( V_1 = 2 \, \text{m}^3 \)
- Final volume, \( V_2 = 0.5 \, \text{m}^3 \)
- Initial pressure, \( P_1 = 4 \times 10^5 \, \text{N/m}^2 \)
- Adiabatic index, \( \gamma = 1.4 \)

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