Question

A sample containing 1.0 mole of an ideal gas is expanded reversibly and isothermally to ten times its original volume in two separate experiments. The expansion is carried out at 300 K and 600 K, respectively. Choose the correct option.

• (A) Work done at 600 K is twice the work done at 300 K.
• (B) Work done at 600 K is 20 times the work done at 300 K.
• (C) Work done at 300 K is twice the work done at 600 K.
• (D) ∆ U ≠ 0 in both cases.

Answer 1

The Correct Option is A

Explanation:
For an ideal gas, the work of reversible expansion under isothermal conditions can be calculated by using the expansion w = -nRT ln Vf/Vi.$\frac{\mathrm{W}600\mathrm{K}}{\mathrm{W}300\mathrm{K}}=\frac{1\times \mathrm{R}\times 600\times \ln \frac{10}{1}}{1\times \mathrm{R}\times 300\times \ln \frac{10}{1}}=2$In isothermal expansion, $\mathrm{\Delta }\mathrm{U}=0$