Efficiency in a thermodynamic cycle

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Homework Help Overview

The discussion revolves around calculating the efficiency of a thermodynamic cycle involving an ideal gas, specifically focusing on the a-b stage of the cycle. Participants are examining the heat transfer and related equations within the context of thermodynamics.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of the Gibbs equation and the ideal gas law to derive expressions for heat transfer during the a-b stage. There are questions regarding the validity of assuming ΔT=0 and the implications of this assumption on the calculations.

Discussion Status

The discussion is ongoing, with participants sharing their calculations and questioning the assumptions made during the derivation. There is an emphasis on exploring the details of the calculations and the potential errors involved.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information available for the calculations. The specific values and conditions of the thermodynamic cycle are not fully detailed in the posts.

Alexandre Ricardo
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I have to calculate the efficiency of the above cycle for an ideal gas, that goes at the order a-b-c-a:
CYCLE.png

I know that the answer is 16/97 but I can't calculate the heat in the a-b stage.
 

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Alexandre Ricardo said:
I have to calculate the efficiency of the above cycle for an ideal gas, that goes at the order a-b-c-a:
View attachment 225655
I know that the answer is 16/97 but I can't calculate the heat in the a-b stage.
Let's see what you have done in detail for the a-b stage.
 
Chestermiller said:
Let's see what you have done in detail for the a-b stage.
Right. I started using the Gibbs equation:
$TdS=PdV+dU$
Using the relation:
∂U/∂v|T=T∂P/∂T|v-P

And making some manipulations I obtained:

dQa-b=cvdT+PdV

Considering an ideal gas. Using the ideal gas state equation, ΔT=0 and PdV=Wa-b.

And I found ΔQ=Wa-b=3P0V0/4

But i think there is something wrong in my calculations and I don't know if I would consider ΔT=0 (even if dT≠0)
 
Alexandre Ricardo said:
Right. I started using the Gibbs equation:
$TdS=PdV+dU$
Using the relation:
∂U/∂v|T=T∂P/∂T|v-P

And making some manipulations I obtained:

dQa-b=cvdT+PdV

Considering an ideal gas. Using the ideal gas state equation, ΔT=0 and PdV=Wa-b.

And I found ΔQ=Wa-b=3P0V0/4

But i think there is something wrong in my calculations and I don't know if I would consider ΔT=0 (even if dT≠0)
Calculate the variation of Q along the path a-b, and see how it varies. Does it change sign along the way?
 

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