Question

One mole of an ideal gas expands isothermally and reversibly from $2$ lit to $20$ lit at $300\, K$. If the final pressure of the gas is $1$ bar, the work done by the gas is

• A. -300 R ln 10
• B. 300 R ln 10
• C. 18
• D. -18

Answer 1

Answer: (A)

Given, $V_{1}=2\, L\, V_{2}=20\, L$
$T=300\, K p_{2}=1\, bar$
Work done for ideal gas expands isothermally and reversibly
$\Rightarrow W=-2303 R T \log \frac{V_{2}}{V_{1}}$
$\Rightarrow W=-R T \ln \frac{V_{2}}{V_{1}}$
$\Rightarrow W=-R \times 300 \ln \frac{20}{2}$
$\Rightarrow W=-300\, R \ln 10$