PSS 19.1 Turn Down the Volume Part C

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In summary, the efficiency of the heat engine is dependent on the amount of heat added to the engine.
  • #1
mantillab
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Homework Statement



A heat engine uses the closed cycle shown in the diagram: (Intro 1 figure) . The working substance is n moles of monoatomic ideal gas. Find the efficiency eta of such a cycle. Use the values for pressure and volume shown in the diagram and assume that the process between points 1 and 3 is isothermal.

117802.jpg


Find the efficiency (eta) of the heat engine.

Homework Equations



PV = nRT
Efficiency (ETA) = Wout/Qh

The Attempt at a Solution


I think I understand the process to get to the solution:
1. Use the ideal gas law to complete your knowledge of n, p, V, and T at one point in the cycle.
2. Use the ideal gas law and equations for specific gas processes to determine p, V, and T at the beginning and end of each process.
3. Calculate Q, W_s, and delta Eth for each process.
4. Find W_out by adding W_s for each process in the cycle. If the geometry is simple, you can confirm this value by finding the area enclosed within the pV curve.
5. Add just the positive values of Q to find Q_H.
6. Verify that net delta Eth=0.
7. Calculate the thermal efficiency eta and any other quantities you need to complete the solution.

The problem that I'm running into is how to find the temperature (T) or the moles of gas (n), with both variables missing, I can't seem to be able to calculate Q or W for any of the processes without at least one of the variables.

Using pV = nRT: n = [pV]/[RT]

Any suggestions? Thanks!
 
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  • #2
You don't have to find all parameters of the working body everywhere. The efficiency is,

[tex]\eta = \frac{W}{Q}[/tex]

so you must (a) find total work [tex]W[/tex] done during one cycle; (b) total heat [tex]Q[/tex] added to the engine during one cycle. Total work is the area enclosed by the loop, I'm sure you can integrate to find that. I'll leave you yourself to decide which part of the loop corresponds to heat added to the system: 1-2, 2-3 or 3-4. If you make a correct decision, the total heat added is also obtained by integrating

[tex]Q = \int P\, dV+\int V\, dP[/tex]

This is problem is not very complicated and should be done in only several steps.
 
  • #3
You won't need to know the number of moles of gas in the system. Just carry the value as n throughout your calculations; when you finally form the quotient for the efficiency, you'll find that n cancels out. (This is physically credible: there is no reason that the efficiency of a process should depend on the mass of gas involved, within reason...)
 
  • #4
Thanks everyone!
 

1. What is PSS 19.1 Turn Down the Volume Part C?

PSS 19.1 Turn Down the Volume Part C is a scientific study conducted to understand the effects of lowering noise levels on human health and well-being.

2. What is the purpose of this study?

The purpose of this study is to determine the potential benefits of reducing noise levels in various environments, including homes, workplaces, and public spaces.

3. How was this study conducted?

The study involved collecting data from a large sample of individuals in different settings, such as homes, offices, and public areas. The noise levels were measured and compared to various health and well-being indicators, such as stress levels, sleep quality, and cognitive performance.

4. What were the major findings of this study?

The study found that reducing noise levels can have significant positive effects on human health and well-being. It was observed that lower noise levels were associated with reduced stress, improved sleep quality, and better cognitive performance.

5. How can the results of this study be applied in real life?

The results of this study can be used to inform noise regulations and policies, as well as guide individuals and organizations in making changes to reduce noise levels in their environments. This can ultimately lead to improved health and well-being for individuals and communities.

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