Increase Carnot Efficiency: Lower Low-Temp Res?

In summary, the conversation discusses the choice between raising the high-temperature reservoir or lowering the low-temperature reservoir in order to increase efficiency in a Carnot heat engine. The discussed formula shows that the greater the temperature difference, the higher the efficiency. However, after experimenting with some numbers, it is noticed that lowering the low-temperature reservoir results in a greater efficiency. While the book suggests raising the high-temperature reservoir, it is concluded that the book may be incorrect. The conversation also explores the effects of T-hot and T-cold approaching infinity and zero, respectively, on efficiency.
  • #1
endeavor
176
0
Suppose you had the choice of either raising the high-temperature reservoir a certain number of kelvins, or lowering the low-temperature reservoir the same number of kelvins. Which would you choose (assuming you wanted to increase the efficiency, of course)?

After doing experimenting with some random numbers, I thought the answer to be: lower the low-temperature reservoir.

For example,
1 - 100/300 = 66.7%
1 - 95/300 = 68.3%
1 - 100/305 = 67.2%
both of the last two are greater than the first, but the second has the greatest efficiency.
However, my book says to raise the high-temperature reservoir. Is my book wrong?
 
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  • #2
Could you tell us what the question asks, exactly? I'm thinking there's something missing. Carnot efficiency approaches 100% as the cold resevoir approaches zero kelvins; for a constant temperature difference, the greatest efficiency will be found for the coldest cold resevoir. This is what you have noticed. But it would take more energy to remove 5 K from the cold than it would to add 5 K to the hot.
 
  • #3
The exact question reads:
"The Carnot efficiency shows that the greater the temperature difference of the reservoirs of a heat engine, the greater the efficiency. Suppose that you had the choice of either raising the high-temperature reservoir a certain number of kelvins, or lowering the low-temperature reservoir the same number of kelvins. Which would you choose (assuming you wanted to increase the efficiency, of course)?"
 
  • #4
The carnot heat engine efficiency is given to us as:

[tex] \eta_{th, rev} = 1 - \frac{T_L}{T_H} [/tex]

What can you conclude?

In other words, what happens as the denominator, [itex] T_H [/itex] approaches infinity? similarly, what happens as the numerator, [itex] T_L [/itex] approaches zero?

Edit: I think you and Chi are right and your book is wrong.
 
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  • #5
I've been over this several ways, but if you look at the other version of the carnot efficiency formula, it seals it:
e=(Thot-Tcold)/ Thot

this says that if the difference in temperature is the same, the greater that T-hot is, the lesser the efficiency is.
 
  • #6
As I am sure you are already aware, your formula is the same thing Chi Meson. The formula[tex] \eta_{th, rev} = 1 - \frac{T_L}{T_H} [/tex] is derived from the reduction of your formula. (Just simplify your fraction)
 
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  • #7
cyrusabdollahi said:
As I am sure you are already aware, your formula is the same thing Chi Meson. The formula[tex] \eta_{th, rev} = 1 - \frac{T_L}{T_H} [/tex] is derived from the reduction of your formula. (Just simplify your fraction)
Yeah. It's just that looking at the other version (of the same thing) it was more obvious to me that the book is incorrect. You can simply say that efficiency is inversely proportional to T hot (if delta T is constant).
 
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  • #8
I thought my book was wrong.
Thanks, all.
 

What is Carnot Efficiency?

Carnot Efficiency is a measure of the maximum possible efficiency of a heat engine or refrigerator, based on the difference in temperature between the hot and cold reservoirs.

Why is it important to increase Carnot Efficiency?

Increasing Carnot Efficiency means that more energy can be converted into useful work, leading to improved energy efficiency and cost savings.

How can Carnot Efficiency be increased?

Carnot Efficiency can be increased by decreasing the temperature of the low-temperature reservoir, which reduces the temperature difference between the hot and cold reservoirs.

What is the role of low-temperature reservoir in Carnot Efficiency?

The low-temperature reservoir is an essential component in Carnot Efficiency, as it serves as the heat sink for the system and determines the maximum possible efficiency.

What are some methods for lowering the low-temperature reservoir?

Some methods for lowering the low-temperature reservoir include using more efficient heat exchangers, insulating the system, and using renewable energy sources that have lower temperatures.

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