2 with the t e mp era tu r e s T 1 < T 2 a r e a v a il a bl e , a nd a t a n y
ID: 797256 • Letter: 2
Question
2 with the temperatures T1 < T2 areavailable, 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 ofheat q2 , transferred from reservoir2 (heat source) to thesystem, 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 thecase 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.
Explanation / Answer
The system returns to its initial state and therefore we can call our entire process a cycle.
To calculate work total
Wtotal = w1 + w2
w = -? Pext dV
w1 = p2( v2 - v1)
w2 = - p1 (v1 -v2)
? Wtotal = p1v2 + p2v2 - p1v1 - p2v1
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.