Thermo, heat transfer rate, power plant

AI Thread Summary
A power plant generating 1300MW at 315 °C must discard heat to a 20 °C sink, which relates to the efficiency of heat engines. The discussion emphasizes the importance of understanding maximum thermal efficiency and the second law of thermodynamics in calculating heat flow. The user initially confuses maximum thermal efficiency with maximum residual heat but later clarifies that using Carnot efficiency can help determine the minimum heat flow. By equating work done per second to the heat discarded, the user can derive the necessary calculations. The conversation highlights the connection between power output and heat transfer in thermodynamic systems.
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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