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  4. The state of an ideal gas is changed as shown, at constant temperature T0. If heat supplied to the gas in process B arrow C is thrice of work done by gas in A arrow B, then the pressure of gas in state C is (P0/2 n) . Find the value of n. <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-45bzvrs7c8lu.png />

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Q. The state of an ideal gas is changed as shown, at constant temperature $T_{0}.$ If heat supplied to the gas in process $B \rightarrow C$ is thrice of work done by gas in $A \rightarrow B,$ then the pressure of gas in state $C$ is $\frac{P_{0}}{2 n}$ . Find the value of $n.$

Question

NTA AbhyasNTA Abhyas 2020Thermodynamics

Solution:

$Q_{B C}=3W_{A B}$
$nRT_{0}ln \frac{P_{B}}{P_{C}}=3nRT_{0}ln ⁡ \left(\frac{P_{0}}{P_{0} / 2}\right)$
$\Rightarrow \, \, \, P_{C}=\frac{P_{0}}{16}$