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Q.

Find the pressure at which temperature attains its maximum value if the relation between pressure and volume for an ideal gas is $P = P_{0} + (1 - α) V^{2}; α > 1$

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a

$P_{0}$

b

$\frac{2 P_{0}}{3}$

c

$\frac{P_{0}}{3}$

d

$\frac{4 P_{0}}{3}$

answer is A.

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Detailed Solution

$\begin{array}{l} P = P_{0} + (1 - α) V^{2} \\ P = P_{0} + (1 - α) \frac{n^{2} R^{2} T^{2}}{P^{2}} \\ P^{2} (P - P_{0}) = (1 - α) n^{2} R^{2} T^{2} \\ T = \frac{P \sqrt{P - P_{0}}}{(\sqrt{1 - α}) nR} \\ \frac{dT}{dP} = 0 \Rightarrow P = \frac{2 P_{0}}{3} \end{array}$

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