Carnot Engine: Finding Final Temperature Attained

[junfan02]

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.

 

[Andrew Mason]

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

 

[junfan02]

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.

 

[junfan02]

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?

 

[Andrew Mason]

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 dQ_h = mcdT_h. The heat flow (into) the cold reservoir will be dQ_c = mcdT_c.

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

 

[junfan02]

The total change in entropy obviously has to be zero since this is a reversible process!

 

[Andrew Mason]

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

 

[junfan02]

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