Question

6 moles of an ideal gas expand isothermally and reversibly from a volume of 1 litre to a volume of 10 liters at 27°C. What is the maximum work done?

• A. 47 kJ
• B. 100 kJ
• C. 63 kJ
• D. 34.465 kJ

Hint:

In an isothermal expansion, the work done can be calculated using the formula \( W = nRT \ln \frac{V_f}{V_i} \).

Answer 1

The Correct Option is D

Step 1: Use the formula for isothermal expansion. The maximum work done in an isothermal expansion is given by: \[ W = nRT \ln \frac{V_f}{V_i} \] Where: - \( n = 6 \, \text{mol} \), - \( R = 8.314 \, \text{J/mol·K} \), - \( T = 273 + 27 = 300 \, \text{K} \), - \( V_f = 10 \, \text{L} \), - \( V_i = 1 \, \text{L} \).
Step 2: Substitute the values: \[ W = 6 \times 8.314 \times 300 \times \ln \frac{10}{1} \] \[ W = 34.465 \, \text{kJ} \]