Thermo, heat transfer rate, power plant

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Homework Help Overview

The discussion revolves around a heat transfer problem related to a power plant generating 1300MW at a temperature of 315 °C, with a heat sink available at 20 °C. Participants are exploring the minimum rate at which heat must be discarded in this context.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to relate the problem to thermodynamic equations and concepts such as dq=Tds and efficiency of a heat engine. Some participants question the interpretation of thermal efficiency and its implications for heat flow.

Discussion Status

Participants are engaged in clarifying concepts related to heat engines and efficiency. There is an acknowledgment of the relationship between work done and heat discarded, with some guidance provided on how to approach the problem using Carnot efficiency.

Contextual Notes

There is an indication of confusion regarding the terms used, particularly in distinguishing between thermal efficiency and residual heat. The discussion also reflects uncertainty about how to incorporate the power output into the calculations.

Confusedby
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Homework Statement


A power plant generates 1300MW and operates at 315 °C a 20°C heat sink is available.
what is the minimum rate at which heat must be discarded?

Homework Equations


not really sure how to begin this one, have a feeling it is related to dq=Tds at constant pressure giving (dq/dT)p=T(dS/dT)p=(dH/dT)p=Cp but that seems to go no where. tried relating it to Enthalpy Changes along the path from 315->100 then condense to liquid water and go 100->20 but none of these seem to use the power out put. honestly completely lost on this one.


The Attempt at a Solution

 
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Hi, Confusedby. Welcome to PF!

This looks like a basic heat engine problem. Have you studied the concept of efficiency of a heat engine and how the second law implies a maximum possible efficiency for given hot and cold reservoir temperatures?
 
Thank You

Well I feel a little silly, for some reason "maximum Thermal efficiency" became "maximum residual heat". If I were to use this arrangement:
(W/e)-W=q residual. were e is the efficiency and W is the work. it should give the minimal heat flow if I assume Carnot Efficiency correct?
 
Yes. q is the heat discarded rather than the rate at which heat is discarded. But if you let W be the work done each second, then q will be the heat discarded each second.
 

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