The internal energy of a monatomic ideal gas is 1.5 nRT. One mole of helium is kept in a cylinder of cross section `8.5 cm^(2)`. The cylinder is closed by a light frictionless piston. The gas is heated slowly in a process during which a total of 42J heat is given to the gas. if the temperature rise through `2^(o)C`, find the distance moved by the piston. atmoshphere pressure `=100 kPa.

Explanation

To solve the problem step by step, we will follow the principles of thermodynamics and the properties of ideal gases.

### Step 1: Understand the internal energy change
The internal energy \( U \) of a monatomic ideal gas is given by the formula:
\[ U = \frac{3}{2} nRT \]
However, in the question, it is stated that the internal energy is \( 1.5 nRT \). This is equivalent to \( \frac{3}{2} nRT \) since \( n = 1 \) mole of helium gas.
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