One mole of an ideal gas undergoes a reversible process: , where and are constants. If its volume in — Thermodynamics and Thermochemistry Chemistry Question
Question
One mole of an ideal gas undergoes a reversible process: $T = T_o + \alpha V$, where $T_o$ and $\alpha$ are constants. If its volume increases from $V_1$ to $V_2$, the amount of heat transferred to the gas is
Answer: C
💡 Solution & Explanation
$P = \frac{RT}{V} = R\left(\frac{T_o}{V} + \alpha\right)$. Work $W = \int_{V_1}^{V_2} P dV = R T_o \ln\left(\frac{V_2}{V_1}\right) + R\alpha(V_2 - V_1)$. Internal energy $\Delta U = C_V \alpha(V_2 - V_1)$. Total heat $Q = \Delta U + W = (C_V + R)\alpha(V_2 - V_1) + R T_o \ln\left(\frac{V_2}{V_1}\right) = C_P \alpha(V_2 - V_1) + R T_o \ln\left(\frac{V_2}{V_1}\right)$.
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