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

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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
[1] 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

  • #2
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Looking at the cycle and given data, what value would you assign to Tc ? What are the possibilities?
 
  • #3
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.
 
  • #4
688
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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.
 
  • #5
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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?
 
  • #6
etudiant
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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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