Two identical containers, A and B, hold equal amounts of the same ideal gas at the same P_o, V_o and T_o. The pressure of A then decreases by a half while its volume doubles; the pressure of B doubles while its volume decreases by a half. Which statement correctly describes the temperatures of the gases after the changes? A) T_A = 0.5T_B = T_o. B) T_B = 0.5T_A = T_o. C) T_B = T_A = T_o. D) T_A = 2T_B = T_o. E) T_B = 2T_A = T_o.

Question

Quizplus · Accepted Answer

According to the ideal gas law, PV = nRT, the temperature of the gas is directly proportional to its pressure and inversely proportional to its volume, as long as the number of moles and the gas constant remain constant. For container A, since the pressure decreases by a half and the volume doubles, the temperature remains the same, as the product of PV stays the same. For container B, since the pressure doubles and the volume decreases by a half, the temperature remains the same again, as the product of PV stays the same. Therefore, the temperatures of the gases in container A and B remain the same as the initial temperature, T_o. So, the correct choice is C.

Two Identical Containers, a and B, Hold Equal Amounts of the Same