acharya

acharya

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RoohNorthern Virginia Community College

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Consider nmoles of ideal gas kept in a cylinder with a piston. Two heat reservoirs 1 and

2 with the temperatures T1 < T2 are available, and at any given moment of time the heat exchange is established with only one of the reservoirs. In the initial equilibrium state the external pressure is p1 , and heat contact is with reservoir 1. At the same time moment the external pressure is quickly changed to

p2 , whereas heat exchange switches to reservoir 2, and we wait for the system to equilibrate. Then the external pressure is quickly returned to its initial value p1 , whereas heat exchange switches back to reservoir 1, and we wait for the system to equilibrate. The system, obviously, returns to its initial state and, therefore we can call our entire process a cycle.

a) Calculate the amount of work wthe system produce on the environment, the amount of heat amount of heat

q2 , transferred from reservoir 2 (heat source) to the system, and the q1 , transferred to reservoir 1 from the system; all for an entire cycle.


b) (2 pts) For given T1 , T2 , and p1 find the range of values for p2 for which the produced work is positive w > 0 .

c) In the case w> 0 our process can be considered as a cycle of a heat engine that produces useful work w > 0 , using the amount of heat q2 from the heat source, and dumping the amount of heat q1 to the reservoir (inevitable loss). Find the efficiency ? = w/q2 of our heat engine.


d) Based on the first and second laws of thermodynamics find the maximal value?max of the efficiency for any heat engine that uses two heat reservoirs at temperatures T1 < T2 . Is our engine more or less efficient? Explain why.
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