Carnot engine efficiency problem

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Homework Help Overview

The discussion revolves around a problem related to the efficiency of a Carnot engine, where heat absorption and exhaustion at specific temperatures are given. Participants are exploring the implications of these values on the temperature at the end of the cycle.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the calculation of efficiency using the Carnot engine formula and question the correct values for heat absorbed and exhausted. There is also a focus on clarifying which point in the cycle is considered the endpoint for determining the temperature.

Discussion Status

Some participants have provided calculations and expressed uncertainty regarding the interpretation of the problem statement. There is an acknowledgment of potential misreading of values, and while calculations have been presented, the exact definition of the endpoint in the cycle remains unclear.

Contextual Notes

Participants are navigating the specifics of the problem statement, including the values for heat absorption and exhaustion, and the implications of these on the final temperature. There is a noted ambiguity about the endpoint of the cycle, which affects the interpretation of the results.

Adriane Baun
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Homework Statement


A Carnot engine absorbed 1.0 kJ of heat at 300 K, and exhausted 400 J of heat at the end of the cycle. What is the temperature at the end of the cycle?

Homework Equations


The efficiency of a Carnot engine is given by the formula
Efficiency = 1 – Qc/Qh
= 1 – Tc/Th

The Attempt at a Solution


Efficiency = 1 – 300J/1000J
= 0.7 = 70%
0.7 = 1 – Tc/Th = 1 – Tc/300K
Tc = 90K
Is it correct? I am trying to self study the topic Carnot cycle for a report
 
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Adriane Baun said:

The Attempt at a Solution


Efficiency = 1 – 300J/1000J
= 0.7 = 70%
0.7 = 1 – Tc/Th = 1 – Tc/300K
Tc = 90K
Is it correct?
Did you mean to use 300 J for QC? The problem statement gives 400 J.

Otherwise, I think your calculation is correct. However, to specify the temperature at the end of the cycle, you need to know which point of the cycle is taken to be the "end of the cycle".
 
Oh i see i misread the problem so it should be
Efficiency = 1 – 400J/1000J = 0.6
Then
0.6 = 1 – Tc/Th = 1 – Tc/300K
Tc = 120K
 
OK. I'm still not clear on which point of the cycle is the endpoint. So I'm not sure if TC is the temperature at the endpoint. But your work for TC looks good.
 

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