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11.Thermodynamics
medium
Figure shows a polytropic process for an ideal gas. The work done by the gas will be in process $AB$ is
A
$\frac{{15}}{2}\,{P_0}{V_0}$
B
$\frac{{14}}{3}\,{P_0}{V_0}$
C
$8\,{P_0}{V_0}$
D
Insufficient information
Solution
$\because P_{1} V_{1}^{x}=P_{2} V_{2}^{x}$
$\frac{16 \mathrm{P}_{0}}{\mathrm{P}_{0}}=\left(\frac{2 \mathrm{V}_{0}}{\mathrm{V}_{0}}\right)^{\mathrm{x}}$
$x=4$
$\mathrm{w}=\frac{\mathrm{P}_{2} \mathrm{V}_{2}-\mathrm{P}_{1} \mathrm{V}_{1}}{1-\mathrm{x}}=\frac{2 \mathrm{P}_{0} \mathrm{V}_{0}-16 \mathrm{P}_{0} \mathrm{V}_{0}}{1-4}$
$=\frac{14}{3} \mathrm{P}_{0} \mathrm{V}_{0}$
Standard 11
Physics
