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One mole of an ideal monatomic gas undergoes a linear process from A to B, in which pressure P and its volume V change as shown in figure, where $V_{0} = 8$ litres. As the volume of the gas is increased, in some range of volume the gas expands with absorbing the heat (the endothermic process); in the other range the gas emits the heat (the exothermic process). Then find the volume (in litres) after which, if the volume of gas is further increased, the given process switches from endothermic to exothermic.

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answer is 5.

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Detailed Solution

$\begin{array}{l} d θ = 0 \\ \frac{n R T}{v_{1}} + p d v = 0 \end{array}$

$\frac{d p}{d v} = - \frac{d p}{v}$

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