Question

1 liter of dry air at STP expands adiabatically to a volume of $3$ litres. If $\gamma =1.4$, the work done by air is ($3^{1.4}=4.655$) (take air to be an ideal gas)

• A. $48J$
• B. $90.5J$
• C. $100.8J$
• D. $60.7J$

Answer 1

The correct option is B $90.5J$

Given, $P_1=1atm$, $T_1=273K$ (At STP)
In adiabatic process,
$$P_1{V}_1^{\gamma }=P_2{V}_2^{\gamma }$$
$$P_2=P_1{\left[\frac{V_1}{V_2}\right]}^{\gamma }$$
$$P_2=1\times {\left[\frac{1}{3}\right]}^{1.4}$$
$$P_2=0.2164atm$$
Work done in adiabatic process is given by
$$\begin{array}{cc}& W=\frac{P_1{V}_1-P_2{V}_2}{\gamma -1}\\ & W=\frac{1\times 1-3\times .2164}{0.4}\times 101.325\end{array}$$
Since, $1atm=101.325kPa$ and $1Liter={10}^{-3}{m}^3$
$$W=89.87J$$