Carnot Engines Question -- Composite Configuration Efficiency

[lc99]

Homework Statement

Homework Equations

The Attempt at a Solution

Trying to figure this out.

So, I'm thinking that adding a extra resevoir for another engine will not add efficiency. It will should split up the W done by the heat reservoir. It just seems to make sense that way. So would the answer be e?

I'm not sure how else to explain the answer.

 

[Dr Dr news]

Calculate the efficiency for each engine, The overall efficiency for multiple processes is the product of the individual efficiencies. Compare to the original efficiency.

 

[Chandra Prayaga]

So, I'm thinking that adding a extra resevoir for another engine will not add efficiency. It will should split up the W done by the heat reservoir. It just seems to make sense that way.

There is no need to guess or "feel" for what makes sense.
In detail, calculate the work done and heat exchanged in each part of the composite engine. You have all the formulas in front of you.

 

[lc99]

Calculate the efficiency for each engine, The overall efficiency for multiple processes is the product of the individual efficiencies. Compare to the original efficiency.

Why is it the product?

 

[Chandra Prayaga]

That can also be checked by completing the calculation as suggested by Dr Dr news

 

[lc99]

That can also be checked by completing the calculation as suggested by Dr Dr news

So far i have Engine A (between TH and TM) a e = 1-TM/TH.
For engine B (between TM and TC) , e =1-TC/TM

 

[Chandra Prayaga]

Start the way the original question posed it. Three temperatures Th, Tm and Tc. One carnot engine operating between Th and Tm, another between Tm and Tc. Now find heat input and output for each engine, work done in each case, as you would for a single engine. Then use the fact that the heat exhaust from the first is the heat input to the second

 

[Dr Dr news]

Just take it one engine at a time. Suppose you have an engine driving a propeller, The engine drives a gear box which in turn drives the propeller. If the engine outputs 250 horsepower and the gear box is 95% efficient then the input to the propeller is 0.95 x 250 HP and if the propeller is 80% efficient then the useful power driving the airplane is 0.95 x 250 HP x 0.80.

 

[lc99]

Start the way the original question posed it. Three temperatures Th, Tm and Tc. One carnot engine operating between Th and Tm, another between Tm and Tc. Now find heat input and output for each engine, work done in each case, as you would for a single engine. Then use the fact that the heat exhaust from the first is the heat input to the second

When i calculate the work for one engine, is it just the difference of Qh-Qc?

 

[Dr Dr news]

Yes.

 

[lc99]

Yes.

I think

Yes.

since here we are dealing with carnot, can i say W = Th-Tc?

 

[lc99]

I think

since here we are dealing with carnot, can i say W = Th-Tc?

Are there any other formulas i need for this. So far i am using W =Th-Tc and e = W/Qh

After writing out the individual engines and calculating the work based on the previous i have:

(Th-W1-Tc) /Th

 

[Dr Dr news]

The work is not equal to the temperature difference. For a Carnot engine, Wk(out) = Q(absorbed) - Q(rejected) and the Carnot efficiency is η = Wk(out) / Q(absorbed) = [Q(absorbed) - Q(rejected)] / Q(absorbed) = (Qa - Qr) / Qa. Further, since this engine operates isentropically, we can relate Qa = Ta ΔS and Qr = Tr ΔS, and finally, η = (Ta ΔS - Tr ΔS) / Ta ΔS = (Ta - Tr) / Ta = 1 - (Tr / Ta). for each engine. For multiple engines η(overall) = η(1) η(2) η(3) ...