Carnot engine efficiency problem

AI Thread Summary
The discussion revolves around calculating the temperature at the end of a Carnot engine cycle, given that it absorbs 1.0 kJ of heat at 300 K and exhausts 400 J. The initial calculation for efficiency was incorrect due to a misinterpretation of the heat exhausted, which should be 400 J instead of 300 J. After correcting the efficiency to 0.6, the temperature at the cold reservoir (Tc) was recalculated to be 120 K. However, there remains some ambiguity regarding which point in the cycle is considered the endpoint for this temperature. Overall, the calculations for Tc appear accurate, but clarification on the cycle's endpoint is needed.
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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