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One mole of an ideal gas is contained under a weightless pistion of a vertical cylinder at a temperature $\mathrm{T}$ . The space over the pistion opens into the atmosphere. What work has to be performed in order to increase isothermally the gas volume under the pistion $\eta$ times
Option: 1
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Option: 2
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Option: 3
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Option: 4
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Answers (1)

best_answer

Let A be the area of cross-section

$\mathrm{F}+\mathrm{PA}=\mathrm{P}_{0} \mathrm{~A}$
$\mathrm{~F}=\left(\mathrm{P}_{0}-\mathrm{P}\right) \mathrm{A}$

Work done by the agent
$\mathrm{W}=\int_{\mathrm{V}}^{n \mathrm{~V}} \mathrm{Fdx}=\int_{\mathrm{V}}^{n \mathrm{~V}}\left(\mathrm{P}_{0}-\mathrm{P}\right) \mathrm{Adx}$
$=\int_{\mathrm{V}}^{n \mathrm{y}}\left(\mathrm{P}_{0}-\mathrm{P}\right) \mathrm{dV}$
$=P_{0}(\eta-1) V-\int_{V}^{\eta V} n R T \frac{d V}{V}$
$=R T(\eta-1)-n \log _{\mathrm{e}} \eta$

Posted by

Deependra Verma

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