Question

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

• A. Work done at 600K is 20 times the work done at 300K.
• B. Work done at 300K is twice the work done at 600K.
• C. Work done at 600K is twice the work done at 300K.
• D. $\Delta U$ = 0 in both cases.

Answer 1

Answer: (C), (D)

The correct options are
C Work done at 600K is twice the work done at 300K.
D $\Delta U$ = 0 in both cases.

$\frac{W_{600K}}{W_{300K}}=\frac{-1\times R\times 600Kln\frac{10}{1}}{-1\times R\times 300Kln\frac{10}{1}}=\frac{600}{300}=2$.
For isothermal expansion of ideal gases, $\Delta U=0$.