What is the Efficiency of a Carnot Refrigerator?

In summary, when viewing the Carnot cycle in reverse, the efficiency becomes the inverse and is no longer a valid measure. Instead, the coefficient of performance (COP) is used to measure the effectiveness of a heat pump or refrigerator. This is because these devices do not do mechanical work, but instead move heat. The COP is always greater than 1, indicating that more heat is moved than the input power. This is not a violation of thermodynamics, but simply a result of the heat engine running in reverse.
  • #1
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In the textbook, it reads: the reverse of carnot cycle is just a refrigerator or heat pump. In this sense, except for the direction of carnot cycle is reverse, could I say the way to calculate the efficiency of the carnot refrigerator is the same? That is, could be still use

[tex]\eta = 1 - \frac{T_{cold}}{T_{hot}}[/tex]

to calculate the efficiency of Carnot refrigerator?

Thanks
 
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  • #2
No: since the cycle is being viewed from the opposite direction (basically), the efficiency is the inverse.
 
  • #3
russ_watters said:
No: since the cycle is being viewed from the opposite direction (basically), the efficiency is the inverse.

You are right. I deduce the efficiency for the Carnot refrigerator similar to the steps for deducing the efficiency for Carnot engine. I've got something like this

[size=+2]
[tex]
\eta = \frac{T_h}{T_h-T_c}
[/tex]
[/size]

But with this expression, if [tex]T_c[/tex] is just a bit below [tex]T_h[/tex] but still be positive, the efficiency will be large than one? How's that possible? How to explanation this? What's the physical significance of this result?
 
  • #4
Well, since these devices don't do mechanical work, the output is moved heat. In fact, for both heat pumps and air conditioners, the amount of heat moved is greater than the input power.
 
  • #5
re Russ Watters:
An air conditioner IS a heat pump -- just turn it around in the window!
iiuc, modern combination A/Cs-heat pumps (Mitsubishi's/Fujitsu's, etc) don't mechanically switch air flows, they re-route the refrigerant through different coils, or some such thing.

To the OP, when you run a heat engine in reverse (ie, A/Cs, heat pumps), you no longer speak of efficiency, but of COP -- coefficient of performance, or whatever else engineers like to call it. And as you observed, it is always greater than 1, just as efficiency is always less than 1.

There is no violation of thermo here, just a statement that if heat can drive a motor, a motor can pump heat. This pumped heat, plus the inevitable decay of the motor's work into heat, gives the appearance of more than you put in, but it really is not.
 
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  • #6
HoloBarre said:
re Russ Watters:
An air conditioner IS a heat pump -- just turn it around in the window!
iiuc, modern combination A/Cs-heat pumps (Mitsubishi's/Fujitsu's, etc) don't mechanically switch air flows, they re-route the refrigerant through different coils, or some such thing.
Different way of saying the same thing, but yes, you are correct. It might lead to a better explanation, for people confused about the COP concept...

If a window air conditioner moves 1 kW of heat energy from the cold coil (the evaporator coil) to the hot coil (condenser coil) while consuming 0.5kW of electrical energy, it dissipates a total of 1.5 kW at the hot coil. That's an efficiency of .5/1.5=.333. Flip it around in the window and you get 1.5 kW of heating for an electrical input of 0.5 kW, or a COP of 1.5/.5=3.0.
 
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1. What is the Reverse of Carnot Cycle?

The Reverse of Carnot Cycle, also known as the Carnot Heat Pump, is a thermodynamic process that operates in the opposite direction of the Carnot Cycle. Instead of producing work from heat, it uses work to transfer heat from a colder reservoir to a hotter reservoir.

2. How does the Reverse of Carnot Cycle work?

The Reverse of Carnot Cycle works by using a series of reversible processes, including isothermal and adiabatic processes, to transfer heat from a colder reservoir to a hotter reservoir. This is achieved by using a working fluid, such as a gas or liquid, to absorb heat from the colder reservoir and then expel it to the hotter reservoir with the help of a mechanical device.

3. What is the efficiency of the Reverse of Carnot Cycle?

The efficiency of the Reverse of Carnot Cycle is given by the formula 1 - (Tc/Th), where Tc is the temperature of the colder reservoir and Th is the temperature of the hotter reservoir. This means that the efficiency of the heat pump increases as the temperature difference between the two reservoirs decreases.

4. What are the applications of the Reverse of Carnot Cycle?

The Reverse of Carnot Cycle has many practical applications, including refrigeration, air conditioning, and heat pumps. It is also used in industrial processes, such as chemical and food processing, to maintain specific temperatures in different parts of a system.

5. Are there any limitations to the Reverse of Carnot Cycle?

While the Reverse of Carnot Cycle is a highly efficient process, it is limited by the temperature difference between the two reservoirs. As the temperature difference decreases, the efficiency of the heat pump decreases as well. Additionally, the efficiency of the heat pump is also affected by the properties of the working fluid and the mechanical efficiency of the device used to transfer heat.

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