Heat Extracted and Delivered to Reservoirs in a Heat Engine

In summary: Is it the proportion of energy that is converted to work? What is the maximum operating temperature for a heat engine? What is the Carnot efficiency?How do you define the efficiency of a heat engine? Is it the proportion of energy that is converted to work? What is the maximum operating temperature for a heat engine? What is the Carnot efficiency?The efficiency of a heat engine is the proportion of energy that is converted to work. The maximum operating temperature for a heat engine is 300K. The Carnot efficiency is 95%.
  • #1
Willfrid Somogyi
21
4
NO TEMPLATE---MISPLACED HOMEWORK

So it seems like a pretty simple question, and in all likelihood it is, but my lecturer somehow managed to miss this bit in his lecture notes.

A heat engine operates between 500K and 300K with 20% of the efficiency of Carnot engine operating between the same temperatures. If the work done per cycle is 100 kJ, calculate:
(i) The heat extracted from the hot reservoir per cycle.
(ii) The heat delivered to the cold reservoir per cycle

Can anyone help?
 
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  • #2
For a Carnot engine operating between these temperatures, what fraction of the heat received from the hot reservoir is released to the cold reservoir? What fraction is converted to work? What is the efficiency?
 
  • #3
Chestermiller said:
For a Carnot engine operating between these temperatures, what fraction of the heat received from the hot reservoir is released to the cold reservoir? What fraction is converted to work? What is the efficiency?
Sorry, to be clear this isn't homework. This is simply a practice question I found elsewhere and I'd like a complete answer if that's possible?
 
  • #4
Willfrid Somogyi said:
Sorry, to be clear this isn't homework. This is simply a practice question I found elsewhere and I'd like a complete answer if that's possible?
You'd like a complete answer, but that's not how we work here at Physics Forums. We help you get the answer yourself by asking you leading questions and giving you hints. If that's not the way you are willing to proceed, then have a nice day.
 
  • #5
Well it's going to be a bit of an issue as I've never been taught it, as mentioned in the original post, so I have no knowledge of any of the theory, hence why I asked for a complete answer.
 
  • #6
Willfrid Somogyi said:
Well it's going to be a bit of an issue as I've never been taught it, as mentioned in the original post, so I have no knowledge of any of the theory, hence why I asked for a complete answer.
Physics Forums is not structured as a venue for providing a complete tutorial on something like this. Maybe, someday, someone will write a Physics Forums Insights article on heat engines, but, as of now, no such article exists.

Tell us more about your situation. What is the academic course that this problem comes from? If heat engines were not covered in your course, are you still expected to be responsible for the material? What textbook are you using in your course, and what other textbooks or online sources have you consulted to develop background for solving this problem?
 
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  • #7
Chestermiller said:
Physics Forums is not structured as a venue for providing a complete tutorial on something like this. Maybe, someday, someone will write a Physics Forums Insights article on heat engines, but, as of now, no such article exists.

Tell us more about your situation. What is the academic course that this problem comes from? If heat engines were not covered in your course, are you still expected to be responsible for the material? What textbook are you using in your course, and what other textbooks or online sources have you consulted to develop background for solving this problem?

It's in the syllabus and a similar question came up in a past paper, I've tried emailing my lecturer but have had no response and being out of term time he won't be available at the University itself. I'm currently on a first year Physics course. I've tried looking in the usual places including this forum, HyperPhysics and a few other online teaching resources but none offered a clear explanation. I don't have access to a textbook as the recommend ones for my course are ~ £160 and I can't afford that. The university library isn't open at the moment or I'd use the textbook there and all my peers are having the same problem as myself.
 
  • #8
How do you define the efficiency of a heat engine?
 

1. What is meant by "heat extracted and delivered to reservoirs in a heat engine"?

"Heat extracted and delivered to reservoirs in a heat engine" refers to the process of converting thermal energy (heat) into mechanical work in a heat engine. This involves extracting heat from a high temperature reservoir and delivering it to a lower temperature reservoir, while converting some of the energy into mechanical work.

2. How does a heat engine work?

A heat engine works by utilizing the principles of thermodynamics to convert heat into mechanical work. This is achieved through a cyclic process involving a high temperature reservoir, a working fluid, and a low temperature reservoir. The working fluid absorbs heat from the high temperature reservoir, expands and does work, and then releases heat to the low temperature reservoir. This cycle is repeated to continuously produce mechanical work.

3. What are the types of heat engines?

There are three main types of heat engines: the steam engine, the internal combustion engine, and the gas turbine. These engines differ in their working fluid and the type of thermodynamic cycle they use to convert heat into work. The steam engine uses water as a working fluid and the Rankine cycle, while the internal combustion engine uses a fuel-air mixture and the Otto or Diesel cycle. The gas turbine uses a compressor, combustion chamber, and turbine to produce work in a Brayton cycle.

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

The efficiency of a heat engine is affected by several factors, including the temperature difference between the high and low temperature reservoirs, the type of working fluid and cycle, and the design and condition of the engine. Generally, a larger temperature difference and a more efficient cycle result in a higher efficiency. However, real engines also experience losses due to friction, heat transfer, and other factors, which can decrease their efficiency.

5. How is heat extracted and delivered to reservoirs in a heat engine measured?

The heat extracted and delivered to reservoirs in a heat engine can be measured using the first and second laws of thermodynamics. The first law states that energy cannot be created or destroyed, only transferred or converted, so the amount of heat extracted from the high temperature reservoir should equal the amount of heat delivered to the low temperature reservoir, minus any work produced. The second law states that heat cannot spontaneously flow from a colder to a hotter body, so the efficiency of the engine can be calculated by dividing the work produced by the heat input from the high temperature reservoir.

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