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P-V Diagrams & Cyclic Processes question from NEET 2018

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P-V Diagrams & Cyclic Processes

The volume (V) of a monatomic gas varies with its temperature (T), as shown in the graph. The ratio of work done by the gas, to the heat absorbed by it, when it undergoes a change from state A to state B, is

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Answer: (a)

The V-T graph is a straight line through the origin, so $V \propto T$ : the process A to B is isobaric.
Work $W = P\Delta V = nR\Delta T$ ; heat $Q = nC_P\Delta T$ with $C_P = \frac{5}{2}R$ for a monatomic gas.
$\frac{W}{Q} = \frac{R}{\frac{5}{2}R} = \frac{2}{5}$
So the answer is (a) $\frac{2}{5}$ .

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