Question

Five gram mol of a diatomic gas $(\gamma =1.4)$ is compressed adiabatically so that its temperature rises from ${127}^{o}C$ to $2{27}^{o}C.$ The work done will be:

• A. $5894.6J$
• B. $10392.5J$
• C. $9875.2J$
• D. $2356.4J$

Answer 1

The correct option is B $10392.5J$

We know, from first law, $\Delta U=q+w$.
For adibatic process, $q=0$.
Also $\Delta U$ = $n{C}_{v}dT$ and w = $\Delta U$ = $\frac{nR}{(\gamma -1)}(T_2-T_1)$
= $\frac{5\times R}{(1.4-1)}(500-400)=10392.5J$