A gas expands in a piston cylinder device from to , the process being described by , where is in , i — Thermodynamics and Thermochemistry Chemistry Question
Question
A gas expands in a piston cylinder device from $V_1$ to $V_2$, the process being described by $PV = a + bV$, where $P$ is in $\text{Nm}^{-2}$, $V$ is in $\text{m}^3$ and $a$ and $b$ are constants. The work done in the process is
Answer: B
💡 Solution & Explanation
$P = \frac{a}{V} + b$. The work done by the gas is $W = -\int_{V_1}^{V_2} P dV = -\int_{V_1}^{V_2} (\frac{a}{V} + b) dV = -[a \ln V + bV]_{V_1}^{V_2} = -a \ln(V_2/V_1) - b(V_2 - V_1)$.
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