Question

A Carnot engine operates between two heat reservoirs at temperatures TH and TC. An inventor proposes to increase the efficiency by running one engine between TH and an intermediate temperature T and a second engine between T and TC using as input the heat expelled by the first engine.
1) Compute the efficiency of this composite system. Express your answer in terms of some or all of the variables T, TH, and TC.
2) Compare the efficiency of this composite system to that of the original engine.

Answer 1

The formula for efficiency of an original carnot engine is;

e = 1 - T(C) /T(H) ——— eq 1

The efficiency is;

e(12) = (W1 + W2)/Q(H1)

Where W1 is work done by 1st engine; W2 is work done by second engine and Q(H1) is the heat input to the first engine.

W = Q(H) + Q(C)

e(12) = [Q(H1) + Q(C1) + Q(H2) + Q(C2)] / Q(H1)

e(12) equation compared to this, QH2 = -QC1

e(12) = [Q(H1) + Q(C1) - Q(C1) + Q(C2)] / Q(H1)

So e(12) = [Q(H1) + Q(C2)] / Q(H1)

So e(12) = 1 + [Q(C2)/Q(H1)] ———eq 2

Also,

Q(C2) /Q(H2) = (-Tc/T')

Q(C2) = -Q(H2) (Tc/T')

This is also equal to Q(C1) (TC/T')

But Q(C1) is also equal to;

-Q(H1) (T'/TH)

Q(C2) = -Q(H1) (T'/TH)(TC/T')

Q(C2) = -Q(H1)(TC/TH)

Replacing this with Q(C2) in eq 2 to obtain;

e(12) = 1 + [[-Q(H1)(TC/TH)] /Q(H1)]

e(12) = 1 - TC/TH

To know more about Carnot engine visit :-

https://brainly.com/question/14680478

#SPJ4