# How Does a Carnot Refrigerator Work Between Different Temperatures?

• ziddy83
In summary, The question is asking about a carnot refrigerator that operates between two heat reservoirs at temperatures of 320K and 270K. The first part of the question asks how many joules of heat energy the refrigerator delivers to the reservoir at 320K if it receives 415J of heat energy from the reservoir at 270K in each cycle. The second part asks for the power input required to operate the refrigerator if it goes through 165 cycles per minute. The solution involves finding the change in entropy over one cycle and using the co-efficient of performance for a refrigerator to calculate the power consumption.
ziddy83
hey everyone,
I need some help solving the following problem. I am kind of confused on where to start. here is the question from the book.

A carnot refrigerator is operated between two heat reservoirs at temperatures of 320K and 270K.

a) If in each cycle the refrigerator receives 415J of heat energy from the reservoir at 270k, how many joules of heat energy does it deliver to the reservoir at 320k?

b)If the fridge goes through 165 cycles each minute, what power input is required to operate the refrigerator?

Thanks in advance for any help.

Anyone...?

What is the efficiency expression for a carnot refrigerator in terms of source and sink temperatures; heat absorbed from source and heat rejected to sink. Equate them and simplify.

How can you know work done from the heat abosrbed and heat rejected? After that it is simple algebra.

ziddy83 said:
Anyone...?

You need to show some work. Think about the two quantities that are conserved in the ideal carnot cycle (hint: it's a reversible process).

ziddy83 said:
hey everyone,
I need some help solving the following problem. I am kind of confused on where to start. here is the question from the book.

A carnot refrigerator is operated between two heat reservoirs at temperatures of 320K and 270K.

a) If in each cycle the refrigerator receives 415J of heat energy from the reservoir at 270k, how many joules of heat energy does it deliver to the reservoir at 320k?

b)If the fridge goes through 165 cycles each minute, what power input is required to operate the refrigerator?

Thanks in advance for any help.
Over one cycle: $$Q_H/T_H + Q_C/T_C = \Delta S$$

What is [itex]\Delta S[/tex] over one cycle? What does that tell you about Q_H?

The co-efficient of performance for a refrigerator is:

$$COP = \frac{Q_C}{W} = \frac{Q_C}{Q_H - Q_C}$$

Can you work W out in terms of temperatures and COP? Find W from that (one cycle) and then work out work consumption in 165 cycles. That is the energy / minute or power.

AM

## What is the Carnot cycle?

The Carnot cycle is a theoretical thermodynamic cycle that describes the most efficient way to convert heat into work. It consists of four reversible processes: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression.

## What is the significance of the Carnot cycle?

The Carnot cycle serves as a standard for measuring the efficiency of real-world heat engines. It also provides insight into the limitations of heat engines and the second law of thermodynamics.

## How does the Carnot cycle work?

The Carnot cycle works by taking in heat from a high-temperature reservoir, converting some of it into work, and releasing the remaining heat to a low-temperature reservoir. This process is repeated in a cycle to produce continuous work.

## What are the key components of the Carnot cycle?

The key components of the Carnot cycle are the two heat reservoirs, a working substance (such as a gas), and a set of reversible processes that the substance undergoes.

## What are the practical applications of the Carnot cycle?

The Carnot cycle is used as a theoretical model to analyze and improve the efficiency of real-world heat engines. It is also used in the design and optimization of refrigeration and heat pump systems.

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