Question

A simple (non-cyclic) heat engine. Consider a cylinder containing an ideal gas under a piston, as shown in Figure below. After a weight m1 is removed from the piston, the gas expands, lifts the remaining weight m2, and the piston eventually settles at a new position h2.

A. Assuming that the above process is carried out in a room whose temperature is maintained constant so that the initial and the final temperature of the gas is exactly the same, what is the work W performed on the weight m2 in this process?

B. What is the heat received by the gas in this process?

C. Think about this contraption as a heat engine that receives heat from the surroundings and performs work. Does its operation contradict the 2nd law? (recall the formulation of the 2nd law that is concerned with heat engines). Explain your answer.

D. What is the change of the Helmholtz free energy of the gas ΔA as a result of the process? E. Compare W with ΔA. Which one is greater? Is your finding consistent with the equation that we have derived in the class for the maximum work that can be performed by a system at constant temperature?

Answer 1

A) The total work done by the system , is equal to the heat put into the system minus the heat taken out .

or where pressure of an ideal gas is

2) Heat ,

is zero in this case, hence Q is zero

3) But sometimes the system takes heat from the surroundings. There exists a thermodynamic variable called entropy which is a natural process that starts in one equilibrium state and ends in another will go in the direction that cause the entropy of system and the environment to increase for an irreversible process and to remain constant for a reversible process; Entropy

4)

We know helmholtz free energy change

dA= -SdT+W

Hence W is greater by a factor of SdT than A