The pressure in monoatomic gas increases linearly from ` =4xx10^(5) Nm^(-2)` to ` 8xx10^(+5) Nm^(-2)` when its volume increases from `0.2m^(3)` to `0.5m^(3)`. Calculate .
(i) Work done by the gas ,
(ii) Increase in the internal energy,
(iii) Amount of heat supplied,
(iv) Molar heat capacity of the gas `R= 8.31J mol^(-1) K^(-1)`

Explanation

To solve the problem step by step, let's break it down into the required parts:

### Given Data:
- Initial pressure, \( P_1 = 4 \times 10^5 \, \text{N/m}^2 \)
- Final pressure, \( P_2 = 8 \times 10^5 \, \text{N/m}^2 \)
- Initial volume, \( V_1 = 0.2 \, \text{m}^3 \)
- Final volume, \( V_2 = 0.5 \, \text{m}^3 \)
- The gas is monoatomic.
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