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

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Discussion Overview

The discussion revolves around calculating the electric output of a nuclear power plant in relation to Carnot efficiency, specifically focusing on the application of thermodynamic principles to a given problem involving temperature variables and efficiency calculations. Participants are exploring the implications of the provided data and equations in the context of a homework assignment.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses confusion over the assignment's variables and the appropriate equations to use, specifically referencing the Carnot efficiency formula η=TH-Tc/TH.
  • Another participant questions what value should be assigned to Tc and discusses the possibilities based on the given data.
  • There is a suggestion that 540°F should be considered as Thot and 60°F as Tcold, though uncertainty remains regarding the relevance of the river input temperature.
  • A participant points out a potential error in temperature conversion, reminding others of the need to use Kelvin or Rankine in efficiency calculations.
  • Some participants clarify that the plant operates at 80% of the Carnot efficiency rather than the Carnot efficiency being 80% itself, leading to discussions about the implications of this interpretation.
  • One participant calculates the optimal Carnot efficiency based on the temperatures provided, arriving at 48% and discussing the practical limitations that reduce the overall electric output to under 40% of the thermal output.

Areas of Agreement / Disagreement

Participants express differing interpretations of the problem statement and the relevant temperatures to use in calculations. There is no consensus on the assignment of Tc or the implications of the efficiency percentages, indicating ongoing debate and uncertainty.

Contextual Notes

Participants note the importance of using appropriate temperature scales (Kelvin or Rankine) for calculations, and there are unresolved questions about the relevance of certain temperature values provided in the problem statement.

goldguy500
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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.
 
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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 I am not sure what the other given numbers of river input temperature 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?
 
gmax137 said:
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.
 
Last edited:

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