Question
Match List-I with List-II
Given $V_{1}$ and $V_{2}$ are initial and final volumes respectively:
| List-I (Isothermal process) | List-II (Expression) | ||
|---|---|---|---|
| A. | Reversible expansion | I. | $$q = 0$$ |
| B. | Free expansion | II. | $$q = nRTln\frac{V_{2}}{{\text{ }V}_{1}}$$ |
| C. | Irreversible Compression | III. | $$w = - p_{\text{ext}\text{~}}\left( V_{1} - V_{2} \right)$$ |
| D. | Cyclic reversible | IV. | $$\frac{q_{\text{rev}\text{~}}}{T} = 0$$ |
Choose the correct answer from the options given below:
Options
Solution
Sol. [Key Concept: Match each isothermal process to its expression: reversible expansion $q = nRTln\frac{V_{2}}{V_{1}}$, free expansion $q = 0$, irreversible compression $w = - P_{ext}(V_{1} - V_{2})$, cyclic $\frac{q_{rev}}{T} = 0$.]
(A)For isothermal process, $\Delta U = 0$
$W = - nRT\mathcal{l}n\left( \frac{V_{2}}{{\text{ }V}_{1}} \right)$ so $q = nRT\mathcal{l}n\left( \frac{V_{2}}{{\text{ }V}_{1}} \right)$
(B) Free expansion which is isothermal must be adiabatic, so $q = 0$
(C) Irreversible process $W = - P_{\text{ext}\text{~}}\left\lbrack V_{2} - V_{1} \right\rbrack$ $\begin{matrix} & \\ & \end{matrix}\ $
(D) Cyclic process, change in state function (S) so change in entropy must be zero $dS = \frac{{dq}_{rev}}{\text{ }T}$
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