A piston can freely move inside a horizontal cylinder closed at both ends. Initially, the piston separates the inside space of the cylinder into two equal parts each of volume V o , in which an ideal

Question

A piston can freely move inside a horizontal cylinder closed at both ends. Initially, the piston separates the inside space of the cylinder into two equal parts each of volume V_o, in which an ideal gas is contained under the same pressure P_o and at the same temperature. What work has to be performed in order to increase isothermally the volume of one part of gas to 3 times that of the other part by slowly moving the piston?

Options:

Answer:

B

Solution:

V_a = 3V_b and V_a + V_b = 2V_o, so V_a = 1.5V_o and V_b = 0.5V_o. Each part has nRT = P_oV_o. Work done on the gases = -P_oV_o[ln 1.5 + ln 0.5] = -P_oV_oln 0.75 = P_oV_oln4/3. Matches (b).

TestHub · Accepted Answer

V a = 3V b and V a + V b = 2V o , so V a = 1.5V o and V b = 0.5V o . Each part has nRT = P o V o . Work done on the gases = -P o V o [ln 1.5 + ln 0.5] = -P o V o ln 0.75 = P o V o ln4/3. Matches (b).

Chemistry - Thermodynamics - I Question with Solution | TestHub

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