# Calculating Power plant's electric output in relation to carnot efficiency

We were assigned a problem in class, but because it was on guest lecturer material, I am unclear of which given numbers and what equations to use. I do know I am supposed to use: η=TH-Tc/TH But I am confused as to why I have been given 4 variables ...Please Help!
Here is the question
 You are building a 3000 MW (thermal; i.e., the amount of heat the reactor makes) nuclear plant in India on a river in the foothills of the Himalayas with water temperature a constant 40°F (due to snow melt). After the river water is used in the plant condenser, it is returned at a temperature of 80°F. Assuming this plant operates at 80% carnot efficiency, what is the electric output at full power? Assume that the steam is 540°F and the condenser is at an average of 60°F.

## Answers and Replies

Looking at the cycle and given data, what value would you assign to Tc ? What are the possibilities?

I was thinking 540 (converted to Kelvin) as Thot and 60 (in kelvin too as Tcold), but Im not sure what the other given numbers of river input tempurature are for.

Check your numbers again. I do not see 540 Kelvin in the data. Remember:

K = C + 273
R = F + 460

Use K or R in efficiency calculations.

I think the problem statement means that this plant operates at 80% of the Carnot efficiency. (Not, "the Carnot efficiency is 80%").

edit: or is that obvious to you already?

etudiant
Gold Member
I think the problem statement means that this plant operates at 80% of the Carnot efficiency. (Not, "the Carnot efficiency is 80%").

edit: or is that obvious to you already?

Exactly.
Optimal Carnot efficiency is (T(i)-T(c))/T(i), in in degrees K or R.

Using those numbers, the optimal efficiency of the plant is ((540+460)-(60+460))/(540+460)= 48%, which would be wonderful if achieved end to end. Unfortunately, the conversion to electric energy is sufficiently sloppy that electric energy produced is under 40% of the thermal output, barring heroic measures.
Using the 80% conversion efficiency would yield 38.4% overall, which is about state of the art.

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