Two moles of nitrogen gas is kept in a cylinder of cross-section area `10 cm^(3)`. The cylinder is closed by a light frictionless piston. Now the gas is slowly heated such that the displacement of piston during process is `50cm`, find the rise in temperature of gas when `200 J` of heat is added in it. (Atmospheric pressure `=100 kPa, R = 25//3 J//mol-K)`

Explanation

To solve the problem step by step, we will use the principles of thermodynamics, particularly the first law of thermodynamics, and the properties of gases.

### Step 1: Understanding the Given Data
- Number of moles of nitrogen gas, \( n = 2 \) moles
- Cross-sectional area of the cylinder, \( A = 10 \, \text{cm}^2 = 10 \times 10^{-4} \, \text{m}^2 \)
- Displacement of the piston, \( \Delta x = 50 \, \text{cm} = 0.5 \, \text{m} \)
- Heat added, \( Q = 200 \, \text{J} \)
- Atmospheric pressure, \( P_0 = 100 \, \text{kPa} = 100 \times 10^3 \, \text{Pa} \)
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