The piston-and-cylinder device of Illustration 3.4-7 is to be operated in reverse to isothermally compress the 1 mol of air. Assume that the weights in the illustration have been left at the heights they were at when they were removed from the piston (i.e., in process b the first 50-kg weight is at the initial piston height and the second is at Δh = ΔV /A = 0.384 m above the initial piston height). Compute the minimum work that must be done by the surroundings and the net heat that must be withdrawn to return the gas, piston, and weights to their initial states. Also compute the total heat and the total work for each of the four expansion and compression cycles and comment on the results.

Illustration 3.4-7

Showing That More Work Is Obtained If a Process Occurs without Friction 

An initial pressure of 2.043 bar is maintained on 1 mol of air contained in a piston-and-cylinder system by a set of weights W, the weight of the piston, and the surrounding atmosphere. Work is obtained by removing some of the weights and allowing the air to isothermally expand at 25°C, thus lifting the piston and the remaining weights. The process is repeated until all the weights have been removed. The piston has a mass of ω = 5 kg and an area of 0.01 m². For simplicity, the air can be considered to be an ideal gas. Assume that, as a result of sliding friction between the piston and the cylinder wall, all oscillatory motions of the piston after the removal of a weight will eventually be damped.

Compute the work obtained from the isothermal expansion and the heat required from external sources for each of the following: 

a. The weight W is taken off in one step. 

b. The weight is taken off in two steps, with W/2 removed each time. 

c. The weight is taken off in four steps, with W/4 removed each time. 

d. The weight is replaced by a pile of sand (of total weight W), and the grains of sand are removed one at a time.

Processes b and d are illustrated in the following figure.