One mole of ideal gas undergoes a linear process as shown in the figure below. Its temperature expressed as a function of volume $V$ is
KVPY 2015, Diffcult
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(c)
Process given is
To find process equation, we use two point form of equation of straight line,
$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$
Here, $(x, y,)=(0, p_0$, and $\left(x_2, y_2\right)=\left(V_0, 0\right)$ Process equation is
$p=p_0-\frac{p_0}{V_0} \cdot V$
As, $\quad p=\frac{R T}{V}$
$\Rightarrow \frac{R T}{V}=p_0-\frac{p_0}{V_0} \cdot V$
$\Rightarrow T=\frac{p_0 V}{R}\left(1-\frac{V}{V_0}\right)$
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