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P-V graph for an ideal gas undergoing polytropic process PV^m = constant is shown here. Find the value of m.

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–3/2

3/2

3/4

5/3

answer is D.

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Detailed Solution

$\begin{array}{l} {PV}^{m} = count; {Pmv}^{m - 1} dv + v^{m} dp = 0 \\ {pmV}^{m - 1} dv = - V^{m} dp; slope = \frac{dp}{dv} = m \frac{p}{V} \\ slope = \tan 37 = \frac{3}{4} = m \frac{P}{V} \Rightarrow m = \frac{3}{2} \end{array}$

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