Question

Work done when 2 mol of an ideal gas is compressed from a volume of 5 m\(^3\) to 2.5 m\(^3\) at 300 K, under a pressure of 100 kPa is

• A. 497.5 kJ
• B. 99.50 kJ
• C. 248.7 kJ
• D. 49.75 kJ

Hint:

In isothermal processes, work done is calculated using the equation \( W = - P \Delta V \), where pressure can be derived from the ideal gas law.

Answer 1

The Correct Option is A

Step 1: Formula for work done in compression.
For an ideal gas undergoing an isothermal compression, the work done \( W \) is given by: \[ W = - P \Delta V \] Where \( P \) is the pressure, and \( \Delta V \) is the change in volume. The ideal gas law relates pressure and volume: \[ P = \frac{nRT}{V} \] For \( n = 2 \, \text{mol} \), \( T = 300 \, \text{K} \), and \( V \) changing from 5 m\(^3\) to 2.5 m\(^3\), we calculate the work done. Substituting into the formula, we get the result: \[ W = 497.5 \, \text{kJ} \]
Step 2: Conclusion.
The correct answer is (A) 497.5 kJ.