An amount of 1 mole of a gas is changed from its initial state (20L, 2atm) to final state (4L, 10atm), respectively. If the change can be represented by a straight line in P-V curve, the maximum tempe

Question

An amount of 1 mole of a gas is changed from its initial state (20L, 2atm) to final state (4L, 10atm), respectively. If the change can be represented by a straight line in P-V curve, the maximum temperature achieved by the gas in the process is (R = 0.08 L-atm/K-mol)

Prashant Kotian · Accepted Answer

Correct answer: B. equation of path line: p = mv + c. slope m = (10 - 2)/(4 - 20) = -0.5. at (20,2): 2 = -0.5(20) + c → c = 12. so, p = -0.5v + 12. t = pv/nr = (-0.5v^2 + 12v)/r. for maximum t, dt/dv = 0 → -v + 12 = 0 → v = 12 l. at v = 12 l, p = 6 atm. t_max = p × v / r = 6 × 12 / 0.08 = 900 k.

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