What is the Temperature of the Low Temperature Reservoir in a Carnot Engine?

In summary, the Carnot engine is a type of engine that uses heat to power a piston. The efficiency of the engine is determined by the entropy loss of the "high" reservoir.
  • #1
JoeSmith1013
5
0

Homework Statement


A Carnot engine moves a piston which applies 5N of force to a rotating disc by moving a piston 0.25cm for
a total of 5W of power. If the high temperature reservoir is 100K, what must the temperature of the low
temperature reservoir be?

Homework Equations


The efficiency of a Carnot engine is given by the formula
e = 1-TLo/THi.

The Attempt at a Solution


I know you can rearrange the efficiency equation and solve for Tlo which is TLo = (1-e)*THi. After this this step I am drawing a blank on what to do next. I know that it gives you the work done by the piston and the power of the engine, but I don't know what to do next.
 
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  • #2
Do you know anything about the carnot cycle besides the efficiency equation?
 
  • #3
Hmm - is there a solution?
The work per carnot cycle is presumably 5N x 0.0025m = 0.0125J.
There are an infinite number of combinations of T2 and Q1 that can provide this work (T2 = low temp, Q1 = high heat) while still satisfying carnot efficiency.
The power of 5W just indicates how many carnot cycles have to be performed per second.
Comments/critiques welcome!
 
  • #4
Rude man/JoeSmith1013, I feel your pain on this one. To let you know where I'm at on this one, I even had to search to find out what a carnot engine was. Maybe the efficiency equation has nothing to do with it. Maybe it has to do with the fact that the gas temperature has to be reduced enough so that when it is warmed up, the gas expansion is sufficient to produce the 5N and 0.25cm. It is possible for a situation where the temperature difference is so small that the gas expansion cannot even produce the 5 N, 0.25 cm movement. So it seems to me that there has to be some minimum temperature delta to accomplish that. Just my $0.02.
 
  • #5
TomHart said:
Rude man/JoeSmith1013, I feel your pain on this one. To let you know where I'm at on this one, I even had to search to find out what a carnot engine was. Maybe the efficiency equation has nothing to do with it. Maybe it has to do with the fact that the gas temperature has to be reduced enough so that when it is warmed up, the gas expansion is sufficient to produce the 5N and 0.25cm. It is possible for a situation where the temperature difference is so small that the gas expansion cannot even produce the 5 N, 0.25 cm movement. So it seems to me that there has to be some minimum temperature delta to accomplish that. Just my $0.02.
There is always some minimum temperature delta required in any engine.
I did notice that the "high" temperature is pretty da**ed low (almost to frozen Nitrogen) which seems odd but I guess there it is.
Th efficiency of a carnot engine is determined by the fact that the entropy loss of the "high" reservoir = entropy gained by the low (lower!) reservoir. The possible combinations of Q1 and T2 I referred to previously is based on this fact.
 
  • #6
I think there is context missing.
Its pretty specific about how the carnot cycles is being implimented so there may be an example in course notes that can help.
 

1. What is a Carnot Engine?

A Carnot Engine is a theoretical heat engine that operates on the Carnot cycle, a reversible thermodynamic cycle. It was developed by French physicist Nicolas Léonard Sadi Carnot in the early 19th century. It is often used as an idealized benchmark for evaluating the efficiency of real heat engines.

2. How does a Carnot Engine work?

A Carnot Engine operates by taking in heat energy from a high-temperature reservoir and converting a portion of it into work. The remaining heat energy is expelled into a low-temperature reservoir. This process is repeated in a cyclical manner to produce continuous work output.

3. What is the efficiency of a Carnot Engine?

The efficiency of a Carnot Engine is determined by the temperatures of the two reservoirs it operates between. It is given by the formula: efficiency = 1 - (Tcold/Thot), where Tcold is the temperature of the low-temperature reservoir and Thot is the temperature of the high-temperature reservoir. The efficiency of a Carnot Engine is always higher than that of a real heat engine operating between the same two temperatures.

4. What are the applications of a Carnot Engine?

Although a Carnot Engine is a theoretical construct, its principles are used in the design and evaluation of real heat engines. It is also used in the study of thermodynamics and is a fundamental concept in the field. Additionally, the Carnot cycle is used as a standard for comparing the efficiencies of different heat engines.

5. What are the limitations of a Carnot Engine?

One of the main limitations of a Carnot Engine is that it is an idealized model and does not take into account real-world factors such as friction, heat loss, and practical constraints. This means that its efficiency cannot be achieved in real heat engines. Additionally, it only operates between two fixed temperatures, which may not be suitable for all applications.

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