Consider the piston–cylinder assembly containing a pure gas shown below. The initial volume of the gas is 0.05 m3, the initial pressure is 1 bar, and the cross-sectional area of the piston is 0.1 m2. Initially the spring exerts no force on the very thin piston.

(a) A block of mass m = 2040 kg is then placed on the piston. The fi nal volume is 0.03 m3, and the fi nal pressure is 2 * 105 Pa. You may assume that the force exerted by the spring on the piston varies linearly with x and that the spring is very “tight,” so that the volume of the gas is never less than the fi nal volume. Precisely draw the process on a PV diagram, labeling it “process A.” Draw the area that represents the work for this process. What is the value of the work?

(b) Consider instead a process in which a block of mass 1020 kg is placed on the piston in the original initial state, and after the gas inside has been compressed another block of mass 1020 kg is placed on the piston. Draw the process on the same PV diagram, labeling it “process B.” Draw the area that represents the work for this process. What is the value of the work?

(c) Describe the process in which it will take the least amount of work to compress the piston.
Draw the process on the same PV diagram, labeling it “process C.” Draw the area that represents the work for this process. What is the value of the work?

Transcribed Image Text:

m= 2040 kg F = -kx Pat atm A = 0.1 m Process A m= 1020 kg m= 1020 kg F = -kx 000 Pat atm A = 0.1 m Process B