Question

The highest temperature of the gas, attained if the pressure of an ideal gas varies according to the law P = P₀ – aV², where P₀ and a are constants, is –

• A. T_max = $\frac{2P_{0}}{2nR}\left( \frac{P_{0}}{3a} \right)^{1/2}$
• B. T_max = $\frac{2}{3}\frac{P_{0}}{nR}\left( \frac{P_{0}}{3a} \right)^{1/2}$
• C. T_max = $\frac{P_{0}}{3nR}\left( \frac{P_{0}}{3a} \right)^{1/2}$
• D. None of these

Answer 1

Answer: (B)

T_max = $\frac{2}{3}\frac{P_{0}}{nR}\left( \frac{P_{0}}{3a} \right)^{1/2}$

Answer 2

P = P₀ – aV² ; Ž PV = mRT , P₀V – aV³ µ m T

$\frac{dT}{dv} = 0$ Ž P₀ – 3aV² = 0 Ž V = $\sqrt{\frac{P_{0}}{3a}}$

P = P₀ – $a\frac{P_{0}}{3a} = \frac{2P_{0}}{3}$ Ž mR $\frac{2P_{0}}{3}\sqrt{\frac{P_{0}}{3a}} = T$