Question

$2m^3$ volume of a gas ($\gamma =1.4$) at a pressure of $4\times {10}^{5}N/m^2$ is compressed adiabatically so that its volume becomes $0.5m^3$. Calculate the work done in process? (Given $4^{1.4}=6.9$)

• A. $1.48\times {10}^{6}J$
• B. $4.5\times {10}^{6}J$
• C. $3.28\times {10}^{8}J$
• D. $4.28\times {10}^{7}J$

Answer 1

The correct option is A $1.48\times {10}^{6}J$

For an adiabatic process :
$P{V}^{\gamma }=constant=k$
here, $V_1=2m^3,V_2=5m^3{P}_1=4\times {10}^{5}N/m^2,$
so using,
$P_1{V}_1^{\gamma }=P_2{V}_2^{\gamma }$
or, $P_2=P_1(\frac{V_1}{V_2}{)}^{\gamma }=4\times {10}^5(\frac{2}{0.5}{)}^{1.4}$

$P_2=2.78\times {10}^{6}N/m^2$
now work done in adiabatic process is given by
$w=\frac{P_2{V}_2-P_1{V}_1}{\gamma -1}$
$w=\frac{2.78\times {10}^6\times 0.5-4\times {10}^5\times 2}{1.4-1}$
$w=\frac{27.8\times 0.5-4\times 2}{0.4}$$\times {10}^5$

$w=1.48\times {10}^{6}J$