A cylindrical container 70 cm long is separated into two compartments by a movab

Question

A cylindrical container 70 cm long is separated into two compartments by a movable partition that is originally clamped in position 45 cm from the right end. The right compartment is initially filled with one liter (i.e., 0.001 m3) of helium gas at a pressure of 5 x 106 Pa. The left compartment is filled with argon gas at 1 x 106 Pa of pressure. Both of these gasses may be considered ideal. The cylinder is submerged in 10 liters of water and the entire system is initially at the uniform temperature of 270 K. When the piston is unclamped, a new equilibrium situation is ultimately reached with the piston in a new position. The entire system is thermally and mechanically isolated and you may ignore the heat capacities of the cylinder and the piston. What is the increase in the temperature of the water (in K) at the new equilibrium? How far (in cm) from the right end of the cylinder will the piston come to rest? What is the increase of the total entropy (in J/K) of the system?

Explanation / Answer

pV = nRT..................Ideal Gas Equation

Let l1 and l2 be the lengths of the right part and left part of cylindre respectively

p1V1 = n1RT1 = p1l1A

p2V2 =n2RT2 = p2l2A

For euilibirium: p1A = p2A

n1RT1 /l1 = n2RT2/l2

Solve for T1 or T2 for change in temperature.

5*106

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