Maximum work done in a Carnot Cycle

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Discussion Overview

The discussion centers around the work done in a Carnot Cycle, particularly comparing the work done by monatomic and diatomic ideal gases. Participants explore the implications of the equations governing the cycle and the conditions under which the work is calculated, including the effects of temperature and pressure ratios.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • Some participants assert that the total work done in a Carnot Cycle is given by the equation -NR(Th-Tc)ln(Vb/Va), questioning whether this implies equal work done by monatomic and diatomic gases due to the lack of dependence on gamma.
  • One participant attempts to establish the ratio of work done by diatomic gas (W') to monatomic gas (W), suggesting it should be 1 based on earlier claims, but notes a discrepancy with textbook information stating the ratio is 1/3.
  • Another participant points out that the textbook may be assuming certain conditions are held constant, prompting a request for clarification on the exact wording of the assumptions.
  • Clarification is provided that Th is 4 times larger than Tc and the pressure ratio is 64, which some participants believe will affect the comparison between the two types of gases.
  • A participant shares their findings, establishing a relationship for the work ratio W'/W in terms of volume ratios and noting that the ratio of VC/VA is 16 based on the pressure ratio.

Areas of Agreement / Disagreement

Participants express differing views on the implications of the work equations for monatomic and diatomic gases, with some agreeing on the need for constant conditions while others highlight discrepancies with established ratios. The discussion remains unresolved regarding the exact relationship between the work done by the two types of gases.

Contextual Notes

Participants note that assumptions regarding temperature and pressure ratios are critical to the analysis, and the discussion reflects varying interpretations of how these factors influence the work done in the Carnot Cycle.

BrianSauce
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Given that in a Carnot Cycle the two adiabatic processes are essentially equal and opposite in magnitude the total work done by the cycle is in the two isotherms. The total work of the system is generally given as -NR(Th-Tc)ln(Vb/Va). Does this mean that the work done by a monatomic ideal gas is the same as the work done by a diatomic ideal gas since there is no dependence on gamma?
 
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BrianSauce said:
Given that in a Carnot Cycle the two adiabatic processes are essentially equal and opposite in magnitude the total work done by the cycle is in the two isotherms. The total work of the system is generally given as -NR(Th-Tc)ln(Vb/Va). Does this mean that the work done by a monatomic ideal gas is the same as the work done by a diatomic ideal gas since there is no dependence on gamma?
Yes. So...?
 
I'm trying to show the ratio of W'/W where W' is the work done by a diatomic gas in one carnot cycle and W is the work done by a monatomic gas in one carnot cycle. Based on the above, shouldn't this ratio be 1? However I see in my textbook that this is 1/3.
 
They must be assuming.toat something is being held constant. What is the exact wording?
 
The exact wording is that the Th is 4 times larger than Tc and the ratio of maximum to minimum pressure is 64, i.e. P1/P3 = 64.
 
BrianSauce said:
The exact wording is that the Th is 4 times larger than Tc and the ratio of maximum to minimum pressure is 64, i.e. P1/P3 = 64.
Okay. The key to this is P1/P3 is fixed. This is going to change things between the monoatomic and the diatomic cases. Work out all the equations in terms of the heat capacities, and see what you get.

Chet
 
This is the work I have done so far. I have established that W'/W = ln(V'B/Va)/ln(VB/VA) and I also found that the ratio of VC/VA = 16 using the pressure ratio. Points A, B, C, and D refer to the same points as 1, 2, 3, and 4 respectively.
 

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