JEE MAIN - Chemistry (2025 - 2nd April Evening Shift - No. 9)
Arrange the following in order of magnitude of work done by the system/on the system at constant temperature.
(a) $\left|w_{\text {reversible }}\right|$ for expansion in infinite stages.
(b) $\left|w_{\text {irreversible }}\right|$ for expansion in single stage.
(c) $\left|\mathrm{w}_{\text {reversible }}\right|$ for compression in infinite stages.
(d) $\left|w_{\text {irreversible }}\right|$ for compression in single stage.
Choose the correct answer from the options given below :
$\mathrm{c}=\mathrm{a}>\mathrm{d}>\mathrm{b}$
$a>c>b>d$
$a>b>c>d$
Explanation
$$\begin{aligned} &\text { For isothermal process }\\ &\begin{aligned} & \left|\mathrm{W}_{\text {reversible }}\right|_{\text {expansion }}=\left|\mathrm{W}_{\text {reversible }}\right|_{\text {compression }} \\ & =-\mathrm{nRT} \ln \frac{\mathrm{~V}_{\mathrm{f}}}{\mathrm{~V}_{\mathrm{i}}} \\ & \left|\mathrm{~W}_{\text {irreversible }}\right|_{\text {expansion }}<\left|\mathrm{W}_{\text {irreversible }}\right|_{\text {compression }} \\ & \mathrm{d}>\mathrm{c}=\mathrm{a}>\mathrm{b} \\ & \left|\mathrm{~W}_{\text {irreversible }}\right|_{\text {expansion }}=-\mathrm{P}_{\text {ext }}\left(\mathrm{V}_{\mathrm{f}}-\mathrm{V}_{\mathrm{i}}\right) \end{aligned} \end{aligned}$$
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Graphical representation
We can compare work by area of PV graph.
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