# Carnot Refrigerator Efficiency and Energy Calculations | Homework Help

• lindsey4
In summary, the ideal refrigerator uses a carnot cycle where the cold reservoir is heated up to a certain temperature and then work is supplied to turn the water into ice. This process exhausts heat into the room, and the more work that is done the higher the temperature the cold reservoir can reach.
lindsey4

## Homework Statement

An ideal refrigerator utilizes a carnot cycle operating between 0 and 25 degrees celsius. To turn 10 kg of water at 0 degrees celsius into 10 kg of ice at 0 degrees celsius,
a) how much heat is exhausted into the room?
b) how much energy must be supplied to the refrigerator?

## Homework Equations

coefficient of performance of carnot refrigerator (Kcarnot): Tc/(Th-Tc)
n (funky n for efficiency thing)=Wout/Qh [but isn't that for engine]
K=Qc/W

## The Attempt at a Solution

I'm guessing part A is Q so I'd have to find that somehow. And, for part B I think you use the last formula I put here and input Q to find W.

lindsey4 said:
coefficient of performance of carnot refrigerator (Kcarnot): Tc/(Th-Tc)
n (funky n for efficiency thing)=Wout/Qh [but isn't that for engine]
An ideal Carnot cycle is reversible, so W is the work, whether it's in or out.
The only thing that changes is how efficiency is defined. Equations not involving η are unchanged.
W = QH (1-TC/TH ) = QC (1-TH/TC )
I'm guessing part A is Q so I'd have to find that somehow.
There are two Qs: QH and QC. Which do you want for part A?

lindsey4 said:

## Homework Statement

An ideal refrigerator utilizes a carnot cycle operating between 0 and 25 degrees celsius. To turn 10 kg of water at 0 degrees celsius into 10 kg of ice at 0 degrees celsius,
a) how much heat is exhausted into the room?
b) how much energy must be supplied to the refrigerator?

## Homework Equations

coefficient of performance of carnot refrigerator (Kcarnot): Tc/(Th-Tc)
n (funky n for efficiency thing)=Wout/Qh [but isn't that for engine]
K=Qc/W
The COP for the refrigerator is output/input where the output is the amount of heat removed from the cold reservoir, Qc and W is the work supplied: COP = Qc/W

Since W = Qh-Qc, and Th/Tc = Qh/Qc, you can express COP in terms of Th and Tc (your expression is correct).

For a) what do you need to find? (hint: it is one of W, Qh or Qc). For b) what do you need to find? (same hint)

AM

Last edited:

## What is a Carnot refrigerator?

A Carnot refrigerator is a type of heat pump that uses the principles of thermodynamics to transfer heat from a cold reservoir to a hot reservoir. It operates on the Carnot cycle, which is a theoretical cycle that is used to determine the maximum possible efficiency of a heat engine or refrigerator.

## How does a Carnot refrigerator work?

A Carnot refrigerator works by using mechanical work to transfer heat from a cold reservoir to a hot reservoir. It does this by using a working substance, such as a gas, that undergoes a series of thermodynamic processes, including compression and expansion, to transfer heat. The working substance is then circulated through a series of heat exchangers to transfer heat from the cold reservoir to the hot reservoir.

## What is the efficiency of a Carnot refrigerator?

The efficiency of a Carnot refrigerator is determined by the Carnot cycle and is given by the equation: efficiency = (T_hot - T_cold)/T_hot, where T_hot is the temperature of the hot reservoir and T_cold is the temperature of the cold reservoir. This means that the efficiency of a Carnot refrigerator is only dependent on the temperature difference between the hot and cold reservoirs and not on the specific working substance used.

## What are the limitations of a Carnot refrigerator?

The main limitation of a Carnot refrigerator is that it can only operate between two specific temperature limits, the hot and cold reservoir temperatures. It also requires a significant amount of mechanical work to operate, making it less practical for real-world applications compared to other types of refrigerators. Additionally, the efficiency of a Carnot refrigerator decreases as the temperature difference between the hot and cold reservoirs decreases.

## How is a Carnot refrigerator different from other types of refrigerators?

A Carnot refrigerator differs from other types of refrigerators in that it is based on the Carnot cycle and has a theoretical maximum efficiency. Other types of refrigerators, such as vapor-compression refrigerators, use different thermodynamic processes and do not have a theoretical maximum efficiency. Additionally, the working substance used in a Carnot refrigerator is not specific, whereas other refrigerators may use specific substances such as refrigerants.

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