A gas is enclosed in a cylindrical vessel fitted with a frictionless piston.the gas is slowly heated for some time. During the process, 10 J of heat is supplied and the piston is found to move out 10cm. Find the increase in the internal energy of the gas, the area of cross section of the cylinder=`4 cm^(2)` and the atmospheric pressure `=100 kPa.`

Explanation

To solve the problem step by step, we will use the first law of thermodynamics and the given data to find the increase in the internal energy of the gas.

### Step 1: Understand the given data
- Heat supplied to the gas (Q) = 10 J
- Displacement of the piston (d) = 10 cm = 0.1 m
- Area of cross-section of the cylinder (A) = 4 cm² = 4 × 10⁻⁴ m²
- Atmospheric pressure (P) = 100 kPa = 100 × 10³ Pa

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