PV Diagram Problem (ideal efficiency vs actual efficiency)

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SUMMARY

The discussion focuses on calculating the ideal and actual efficiency of a thermodynamic cycle represented on a PV diagram for 4.87 moles of an ideal gas. The ideal efficiency was calculated to be 67% using the formula 1 - TL/TH, where TL is the lower temperature (400K) and TH is the higher temperature (1200K). To find the actual efficiency, participants emphasized the need to determine the heat flow in (Qin) and work output (Wout) by analyzing the heat transfer during different segments of the cycle. The discussion highlights the importance of applying the first law of thermodynamics and understanding the relationships between heat flow, work, and internal energy changes.

PREREQUISITES
  • Understanding of PV=nRT for ideal gas calculations
  • Familiarity with thermodynamic efficiency formulas, specifically η = W/Qh
  • Knowledge of the first law of thermodynamics
  • Concepts of heat flow in constant volume and constant pressure processes
NEXT STEPS
  • Calculate heat flow (Qin and Qout) for each segment of the cycle using Cv and Cp
  • Explore the relationship between internal energy changes and work done during isothermal processes
  • Study the differences between Carnot cycles and non-Carnot cycles in thermodynamics
  • Investigate the application of the first law of thermodynamics in various thermodynamic processes
USEFUL FOR

Students studying thermodynamics, mechanical engineers, and anyone involved in analyzing the efficiency of thermodynamic cycles.

stonecoldgen
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Homework Statement


The PV diagram below (I will describe it) shows a cycle for 4.87moels of an ideal gas. The path ab is along an isothermal line.

Pressure is in atm and volume in m3


Point a: (.08, 6)
Point b: (.24,2)
Point c: (.08, 2)


Find the ideal and the actual efficiency of the cycle

Homework Equations


1atm=101,300Pa
PV=nRT
1-TL/TH=\epsilon
\epsilonactual=Wout/Qin




The Attempt at a Solution


First of all, convert the pressures in atm to Pascals, to make life easier.


The temperature at a and b is 1,200K, the temperature at c is 400K. (found with PV=nRT)

so i thought that plugging that into 1/TL/TH=\epsilon would give me the ideal efficiency. I got 67%


However, I don't know how to get the actual efficiency. I don't know what Qin and Wout are exactly
 
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stonecoldgen said:
Find the ideal and the actual efficiency of the cycle

Homework Equations


1atm=101,300Pa
PV=nRT
1-TL/TH=\epsilon
\epsilonactual=Wout/Qin

The Attempt at a Solution


First of all, convert the pressures in atm to Pascals, to make life easier.

The temperature at a and b is 1,200K, the temperature at c is 400K. (found with PV=nRT)

so i thought that plugging that into 1/TL/TH=\epsilon would give me the ideal efficiency. I got 67%
I will assume that this is an engine cycle so it goes from c to b to a back to c.

Efficiency is η = W/Qh = Qh-Qc/Qh

You cannot use η = 1 - Tc/Th because this is not a Carnot cycle.

So you have to determine Qh and either Qc or W.

Let's try to calculate heat flow in and out. We start by finding which parts of the cycle involve heat flow in and out.

Does heat flow into the gas during ba? How about ac? cb? Hint: Apply the first law.

When does heat flow OUT of the gas? (hint: again apply the first law).

Next, we have to calculate the heat flow IN and the heat flow OUT. To do this we have to know the relationship between heat flow and work or change in internal energy. Cv and Cp and ΔT are used to determine the heat flow in constant volume and constant pressure processes. For the isothermal part, does the internal energy change? So what is the relationship between heat flow and work in this part?

Finally, when you determine the Qh and Qc apply the efficiency formula to determine efficiency, η.AM
 

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