Arrange the following in order of magnitude of work done by the system / on the system at constant temperature : (a) $\left|\mathrm{w}_{ ext {reversible }} ight|$ for expansion in infinite stage. (b) $\left|w_{ ext {irreversible }} ight|$ for expansion in single stage. (c) $\left|w_{ ext…

Question

Arrange the following in order of magnitude of work done by the system / on the system at constant temperature :
(a) $\left|\mathrm{w}_{\text {reversible }}\right|$ for expansion in infinite stage.
(b) $\left|w_{\text {irreversible }}\right|$ for expansion in single stage.
(c) $\left|w_{\text {reversible }}\right|$ for compression in infinite stage.
(d) $\left|w_{\text {irreversible }}\right|$ for compression in single stage.
Choose the correct answer from the options given below:

Aicharya · Accepted Answer

For isothermal process
$\begin{aligned}
& \left|\mathrm{W}_{\text {reversible }}\right|_{\text {expansion }}=\left|\mathrm{W}_{\text {reversible }}\right|_{\text {compression }} \\
& =-\mathrm{nRT} \ln \frac{\mathrm{~V}_{\mathrm{f}}}{\mathrm{~V}_{\mathrm{i}}} \\
& \left|\mathrm{~W}_{\text {irreversible }}\right|_{\text {expansion }} \lt \left|\mathrm{W}_{\text {irreversible }}\right|_{\text {compression }} \\
& \mathrm{d} \gt \mathrm{c}=\mathrm{a} \gt \mathrm{b} \\
& \left|\mathrm{~W}_{\text {irreversible }}\right|_{\text {expansion }}=-\mathrm{P}_{\text {ext }}\left(\mathrm{V}_{\mathrm{f}}-\mathrm{V}_{\mathrm{i}}\right)
\end{aligned}$

We can compare work by area of PV graph

Arrange the following in order of magnitude of work done by the system / on the system at constant…

Solution