Question

For a gas having initial state pressure as 500 Pa expands in a piston-cylinder arrangement from its initial state to the final state at which pressure is 280 Pa. If the relationship between the pressure and volume of the gas is $p^{1.4}V=76.2$. The work for the process will be _____J.

• A. $9.67\text{Joule}$
• B. $0\text{Joule}$
• C. $5.7958\text{Joule}$
• D. $10\text{Joule}$

Answer 1

The correct option is C $5.7958\text{Joule}$

$\text{Work}=\int PdV=\int {\left(\frac{76.2}{V}\right)}^{1/1.4}dV={76.2}^1/1.4{\int }_{0.012688}^{0.02857}\left(V^{-1/1.4}\right)dV$

$=(76.2{)}^{1/1.4}{\left[\frac{\frac{1}{V^{1.4}}+1}{-\frac{1}{1.4}+1}\right]}_{0.012688}^{0.02857}$

$=(76.2{)}^{1/1.4}{\left[\frac{V^{0.2857}}{0.2857}\right]}_{0.012688}^{0.02857}$

$=77.329\left[\right(0.02857{)}^{0.02857}-\left(0.012688{)}^{0.2857}\right]$

$=77.329[0.36212-0.28717]$

$=5.7958\text{Joule}$