ThermodynamicsHard
Question
A gas expands reversibly in a piston cylinder device from V1 to V2, the process being described by PV = a + bV, where P is in Nm–2, V is in m3 and a and b are constants. The work done in the process (w) is
Options
A.$a\log_{e}\left( \frac{V_{1}}{V_{2}} \right) + b\left( V_{2} - V_{1} \right)$
B.$- a\log_{e}\left( \frac{V_{2}}{V_{1}} \right) - b\left( V_{2} - V_{1} \right)$
C.$- a\log_{e}\left( \frac{V_{1}}{V_{2}} \right) - b\left( V_{2} - V_{1} \right)$
D.$a\log_{e}\left( \frac{V_{2}}{V_{1}} \right) + b\left( V_{2} - V_{1} \right)$
Solution
$w = - \int_{V_{1}}^{V_{2}}{P.dv} = - \int_{V_{1}}^{V_{2}}\left( \frac{a}{V} + b \right)dv$
$= - a\ln\frac{V_{2}}{V_{1}} - b\left( V_{2} - V_{1} \right)$
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