Five moles of an ideal gas taken in a Carnot engine working between `100^(@)C` and `30^(@)C`. The useful work done in one cycle is 420 joule. If the ratio of the volume of the gas at the end and beginning of the isothermal expansion is `115/x`. Find the value of x.
(Take R=8.4J/mol.K)

Explanation

To solve the problem, we need to analyze the Carnot engine and the isothermal expansion of the ideal gas. Here are the steps to find the value of \( x \):

### Step 1: Convert temperatures to Kelvin
The Carnot engine operates between two temperatures:
- \( T_1 = 100^\circ C = 373 \, K \)
- \( T_2 = 30^\circ C = 303 \, K \)

### Step 2: Use the efficiency of the Carnot engine
...