Carnot Engine: Finding Final Temperature Attained

AI Thread Summary
A Carnot engine operates between two reservoirs at temperatures T1 and T2, with T1 greater than T2, and equal heat capacities. The discussion focuses on finding the final temperature when both reservoirs reach equilibrium and analyzing the total entropy change, which should be zero due to the reversible nature of the process. Participants suggest calculating the heat flow and changes in temperature for both reservoirs, emphasizing the need to integrate to find the total change in entropy. The key takeaway is that the sum of the entropy changes for both reservoirs must equal zero. The conversation encourages collaboration for problem-solving as participants work through the calculations.
junfan02
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A Carnot engine is operating between a source and a sink at temperatures T1 & T2 (T1>T2) respectively..
The heat capacities of the source and the sink are equal.
Find the final temperature attained.
 
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junfan02 said:
A Carnot engine is operating between a source and a sink at temperatures T1 & T2 (T1>T2) respectively..
The heat capacities of the source and the sink are equal.
Find the final temperature attained.
You have to show us what you have done to solve the problem. Please follow the homework template.

What can you say about the change in total entropy of the two reservoirs at the end when they reach the same temperature? Does that help you find the temperature?

AM
 
I assumed an infinitesimal amount of heat dQ taken away from the reservoir.. So the amount of heat dumped into the sink is T2*dQ/T1.
I couldn't proceed further.
 
dQ amount of heat taken away from the aource reduces its temperature by dQ/c.
Assuming c to be the common heat capacity. And the increase in temperature of the sink for this cycle is T2*dQ/(T1*c)
How do I proceed after this?
 
junfan02 said:
dQ amount of heat taken away from the aource reduces its temperature by dQ/c.
Assuming c to be the common heat capacity. And the increase in temperature of the sink for this cycle is T2*dQ/(T1*c)
How do I proceed after this?

Assume that the temperature changes of the reservoirs during a single cycle are very small. In one cycle the heat flow (out) of the hot reservoir will be dQh = mcdTh. The heat flow (into) the cold reservoir will be dQc = mcdTc.

What is the change in entropy in one cycle?

Can you integrate to Tfinal to determine the total change in entropy over the whole process? Since this is a Carnot engine, what can you say about the total change in entropy?

AM
 
The total change in entropy obviously has to be zero since this is a reversible process!
 
junfan02 said:
The total change in entropy obviously has to be zero since this is a reversible process!
So work out the expression for the change in entropy of each reservoir and set their sum equal to 0!

AM
 
Last edited:
Thanks a lot!
Will give it a try, please be there if I am stuck somewhere..
 

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