Thermodynamics: Efficiency for Stirling engine

In summary: Yes, but the heat flow occurring in 2-3 is an out flow so it wouldn't be included in the efficiency calculation which is based on only on the heat input, right?I believe Qh=5/2*R*n*(Th-Tl)+R*n*Th*ln(r) in the denominatorwhy is that? isn't nRThln(r) the work done from 1-2?http://www.pha.jhu.edu/~broholm/l39/node5.html The heat flow occurring in 2-3 is an out flow, so it wouldn't be included in the efficiency calculation which is based on only on the heat
  • #1
armolinasf
196
0

Homework Statement



I'm trying to find an expression for the efficiency of a stirling engine operating with an ideal diatomic gas, and cycling through a volume V and a multiple of its compression ratio, r, Vr.

Homework Equations



processes:

1-2 isothermal expansion
2-3 isochoric cooling
3-4 isothermal compression
4-1 isochoric heating

r=compression ratio
Th=high temperature
Tl=low temperature

Work=W1 proc. 1-2 (nRTh)ln(r)
Work=W2 proc. 3-4 (nRTl)ln(1/r)
Work Net= W1-W2= nRln(r)(Th-Tl) since ln=-ln(1/r)

Heat Input=Qh=nCv(Th-Tl)=(5/2)R(Th-Tl)

Efficiency=e=W Net/Heat Input=[nRln(r)(Th-Tl)]/[(5/2)nR(Th-Tl)

Canceling:e=(5/2)ln(r)

This does not Make sense since efficiency for an engine with an equal compression ration of say r=10 operating at a Temp high of 300k and low of 200k would have a carnot efficiency of (1/3) while with the above equation e=.92 which is impossible.
 
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  • #2
armolinasf said:
Heat Input=Qh=nCv(Th-Tl)=(5/2)R(Th-Tl)
You are assuming that heat flow into the gas occurs only in the 4-1 constant volume part. Apply the first law to the isothermal expansion (1-2): ΔQ = ΔU + W;

AM
 
  • #3
Yes, but the heat flow occurring in 2-3 is an out flow so it wouldn't be included in the efficiency calculation which is based on only on the heat input, right?
 
  • #4
I believe Qh=5/2*R*n*(Th-Tl)+R*n*Th*ln(r) in the denominator
 
  • #5
why is that? isn't nRThln(r) the work done from 1-2?
 
  • #6
http://www.pha.jhu.edu/~broholm/l39/node5.html [Broken]

This site might be helpful
 
Last edited by a moderator:
  • #7
armolinasf said:
why is that? isn't nRThln(r) the work done from 1-2?
Exactly. Since it is isothermal, ΔU = 0. So, by the first law, ΔQ1-2 = W1-2 (where W = the work done BY the gas). You can see from the first law that heat flow into the gas occurs from 4-1 AND from 1-2.

AM
 
  • #8
armolinasf said:
Yes, but the heat flow occurring in 2-3 is an out flow so it wouldn't be included in the efficiency calculation which is based on only on the heat input, right?
I did not say 2-3. I said 1-2. Apply the first law. You will see that there is positive heat flow into the gas from 1-2.

AM
 

1. What is thermodynamics?

Thermodynamics is the branch of physics that deals with the relationships between heat, work, temperature, and energy. It studies how energy is transferred and transformed in various systems, and how these processes affect the properties of matter.

2. What is efficiency in the context of a Stirling engine?

Efficiency in a Stirling engine refers to the ratio of the engine's output power to its input power. It is a measure of how well the engine converts heat energy into mechanical work. The higher the efficiency, the more energy-efficient the engine is.

3. How is efficiency calculated for a Stirling engine?

The efficiency of a Stirling engine can be calculated by dividing the engine's output power by its input power, and then multiplying by 100 to get a percentage. The input power is usually the heat energy supplied to the engine, while the output power is the mechanical work produced by the engine.

4. What factors affect the efficiency of a Stirling engine?

The efficiency of a Stirling engine can be affected by various factors, including the temperature difference between the hot and cold ends of the engine, the design and materials used in the engine, and the amount of heat energy supplied to the engine.

5. How can the efficiency of a Stirling engine be improved?

The efficiency of a Stirling engine can be improved by optimizing the design and materials used, increasing the temperature difference between the hot and cold ends, and using a more efficient heat source. Regular maintenance and proper tuning of the engine can also help improve its efficiency.

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