Question

Two moles of an ideal monoatomic gas at ${27}^{o}C$ occupies a volume of $V$. If the gas is expanded adiabatically to the volume $2V$, then the magnitude of work done by the gas will be $(\gamma =5/3)$:

• A. $2967.23J$
• B. $2768.56J$
• C. $2500J$
• D. $2800J$

Answer 1

Answer: (B)

$2768.56J$

In adiabatic process,

$T{V}^{\gamma -1}=cons\tan t$

$T_1{V}_1=T_2{V}_2$

$300\times {\gamma }^{\frac{5}{3}-1}=T_2{\left(2V\right)}^{\frac{5}{3}}$

$T_2=\frac{300}{2^{\frac{2}{3}}}$

$=188.7$

$=189K$

Now, work done is given by

$W=\frac{nR(T_1-T_2)}{\gamma -1}$

$=\frac{2\times 8.314\times (300-189)\times 3}{2}$

$=2768.56J$