# Homework Help: Carnot engine

1. Dec 30, 2013

### 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.

2. Dec 30, 2013

### Andrew Mason

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

3. Dec 30, 2013

### 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.

4. Dec 30, 2013

### 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?

5. Dec 30, 2013

### Andrew Mason

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

6. Dec 30, 2013

### junfan02

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

7. Dec 30, 2013

### Andrew Mason

So work out the expression for the change in entropy of each reservoir and set their sum equal to 0!

AM

Last edited: Dec 31, 2013
8. Dec 31, 2013

### junfan02

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