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  • The volume versus temperature graph of two moles of helium gas is shown in the figure. The ratio of heat absorbed and the work done by the gas in proven 1.2 is - <img alt="" src="https://

The volume versus temperature graph of two moles of helium gas is shown in the figure. The ratio of heat absorbed and the work done by the gas in proven 1.2 is -

Option: 1

3


Option: 2

\frac{5}{2}


Option: 3

\frac{5}{3}


Option: 4

\frac{7}{2}


Answers (1)

best_answer

V-T graph is a straight line passing through the origin. Hence,

V \alpha T \text { or } P=\text { constant. }

\begin{aligned} & \therefore d Q=n C_{P} d T \text { and } d U=n C_{V} d T \\ & d \omega=d q-d v \\ & =n\left(c_{p}-c_{v}\right) d T \\ & \therefore \frac{d Q}{d \omega}=\frac{n_{c_{p} d T}}{n\left(c_{p}-c_{v}\right) d T}=\frac{c_{p}}{c_{p}-c_{v}}=\frac{1}{1-\frac{c_{v}}{c_{p}}} \end{aligned}

\therefore \frac{C_{v}}{C_{P}}=\frac{3}{5} for helium gas

\therefore \frac{d Q}{d \omega}=\frac{1}{1-3 / 5}=\frac{5}{2}

Posted by

himanshu.meshram

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