Question

At $27{}^{\circ }C$, $8g$ of helium occupies a volume $V$. The gas expands adiabatically to $8V$, then the work done by gas during expansion is approximately equal to

• A. 5610 J
• B. 3785 J
• C. 6125 J
• D. 4385 J

Answer 1

The correct option is A 5610 J

$T{V}^{\gamma -1}=\text{Const}300.V^{\gamma -1}=T.(8V{)}^{\gamma -1}300.V^{\gamma -1}=T{8}^{\gamma -1}.V^{\gamma -1}T=\frac{300}{8^{\gamma -1}}[\gamma =\frac{Cp}{C_V}=\frac{5}{3}]=\frac{300}{8^{2/3}}=\frac{300}{4}=75KW=-n\frac{R}{\gamma -1}[\Delta T]=-2\times \frac{8.31}{2/3}(-225)=\text{/}2\times \frac{8.31\times 3}{\text{/}2}\times 225=25\times 225W=5610J$