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  • Volume versus temperature graph of two moles of Helium gas as shown in figure. <img alt="" src="https://cdn.entrance360.com/media/uploads/2023/08/19/15q.png" style="height:306px; width:35

Volume versus temperature graph of two moles of Helium gas as shown in figure.

The ratio of the heat absorbed and the work done by the gas in proven 1-2 is ____.

Option: 1

3


Option: 2

5 / 2


Option: 3

5 / 3


Option: 4

7 / 2


Answers (1)

best_answer


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

Hence, V \propto T\\ or ~P= constant.

\begin{aligned} \therefore d Q & =n C_p d t \text { ~and~ } d U=n C_V d T \\ \therefore d \omega & =d Q-d U \\ & =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-C_v} \end{aligned}
For helium. gas,

 \frac{C_v}{C_p}=\frac{3}{5}

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

Posted by

sudhir kumar

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