Consider the piston-cylinder assembly containing a pure ideal gas shown below. The initial volume of the gas is 0.05m3, the initial pressure is 1 bar, and the cross-sectional area of the piston is 0.1m2. Initially the spring exerts no force on the very thin (i.e., massless) piston. a. A block of mass m=2040kg is then placed on the piston. The final volume is 0.03 m3, and the final pressure is 2105Pa. 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 final 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? [Hint: First find the value of the spring constant, k.] b. Consider instead a process in which a block of mass 1020kg is placed on the piston in the original initial state, and after the gas inside has been compressed another block of mass 1020kg is placed on the piston. Draw the process on the same PV diagram as in (a), labeling it "process B." Draw the area that represents the work for this process. What is the value of the work? For these processes, you may assume that PVc= constant, where " c " is a constant that you must determine. 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? Consider the piston-cylinder assembly containing a pure ideal gas shown below. The initial volume of the gas is 0.05m3, the initial pressure is 1 bar, and the cross-sectional area of the piston is 0.1m2. Initially the spring exerts no force on the very thin (i.e., massless) piston. a. A block of mass m=2040kg is then placed on the piston. The final volume is 0.03 m3, and the final pressure is 2105Pa. 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 final 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? [Hint: First find the value of the spring constant, k.] b. Consider instead a process in which a block of mass 1020kg is placed on the piston in the original initial state, and after the gas inside has been compressed another block of mass 1020kg is placed on the piston. Draw the process on the same PV diagram as in (a), labeling it "process B." Draw the area that represents the work for this process. What is the value of the work? For these processes, you may assume that PVc= constant, where " c " is a constant that you must determine. 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
