Efficiency of engine taking diatomic ideal gas through cycles

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Homework Help Overview

The discussion revolves around determining the thermal efficiency of an engine operating with n moles of diatomic ideal gas through a specified thermodynamic cycle. Participants are exploring the relationships between heat, work, and temperature within the context of this cycle.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to find temperatures at various points in the cycle without having specific pressure or volume values. There is a focus on calculating heat absorbed and net work done during the cycle.

Discussion Status

The discussion is ongoing, with participants providing insights into the processes involved in the cycle and questioning how to derive temperatures from given relationships. Some guidance has been offered regarding the calculation of heat absorbed in different processes, but there is no explicit consensus on the approach to take.

Contextual Notes

Participants are working under constraints of missing numerical values for pressure and volume, which complicates their ability to calculate temperatures directly. The efficiency value mentioned is noted as being less than one, indicating a focus on understanding the underlying principles rather than arriving at a definitive solution.

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Homework Statement



What is the thermal efficiency of an engine that operates by taking n moles of diatomic ideal gas through the cycle 1 -------> 2 -------> 3 -------> 4 ------> 1 shown in the figure ?

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Homework Equations



e = W/Qh



The Attempt at a Solution




I know the answer is 10.5

I am trying to prep for a test today and this is the last thing from my homework that I don't understand...can someone explain to me how the answer is generated? I am sort of lost on it and I figure it has to be easier than it seems.
 
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There are two isochoric and two isobaric processes in the cycle. Find temperatures at all four points and calculate the heat absorbed from the source and the net work done.
The efficiency is always less than one thus it must be 10.5%.
 
How to find temp with no p or v numbers?
 
It is P0V0/nR at 1.
 
I'm still confused...po is not a numerical value.
 
say P0V0/nR = T0 then what are temperatures at 2, 3 and 4 ?
 
these are 2T0, 4T0 and 2T0 respectively.
Now find the heat absorbed in isochoric and isobaric processes using Q = n Cv ΔT and Q = n Cp ΔT
 

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