# Carnot Cycle: Analysis of Energy Exchange

• physics123
In summary, in a Carnot cycle, a refrigerator absorbs 120 J of energy at a temperature Tc and does 300 J of work while undergoing the cycle. This means that 300 J of work must equal the heat expelled, and any heat added (120 J) must also be expelled. For a heat engine operating on a Carnot cycle, if it absorbs 420 J of energy while expanding in contact with a hot reservoir at temperature Th and does a net 300 J of work, the remaining 120 J must be expelled as heat. This is because, according to the Carnot cycle, what goes in must come out as either work or heat.
physics123
A refrigerator operates on a Carnot cycle. In this cycles, it absorbs 120 J of energy at a temperature Tc while 300 J of work is done on the gas undergoing the cycle.

How much energy is exhausted as heat during this process?

The answer is 420 J.

I am unsure of where to start for this question as we are not given temperatures.

Recall that, in any cyclic process, the gas must return to its original state. So, in one cycle,

$$\Delta U=Q-W=0$$

Therefore, work done (300 J) must equal heat expelled. And any heat added (120 J) must also be expelled.

zenmaster99 said:
Recall that, in any cyclic process, the gas must return to its original state. So, in one cycle,

$$\Delta U=Q-W=0$$

Therefore, work done (300 J) must equal heat expelled. And any heat added (120 J) must also be expelled.

so to find energy exhausted as heat, it is as simple as adding the work plus any heat added?

physics123 said:
so to find energy exhausted as heat, it is as simple as adding the work plus any heat added?

Could you then explain this question?
A heat engine operates on a Carnot cycle. In this cycles, it absorbs 420J of energy while it expands in contact with a reservoir of temperature Th. The heat engine does a net 300J during the full cycle.

The answer is 120J, so why isn't the energy added? What is the difference between absorbing energy at Th and Tc?

In this case, the engine takes in 420 J from the hot reservoir. This must be expelled as either heat or work. 300 J is returned as work, therefore 120 J must be heat.

Hang on, let me look for the diagram I'm thinking of...

Here it is: https://en.wikipedia.org/wiki/Heat_engine#/media/File:Heat_engine.png

Notice that what goes in must come out as either work or heat. Although this diagram tries to be all-encompassing by including a little loss mechanism, you needn't worry about that at this level.

physics123

## 1. What is the Carnot Cycle?

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

## 2. How does the Carnot Cycle work?

In the Carnot Cycle, a gas is contained in a cylinder with a movable piston. The gas is first heated at a constant temperature (isothermal expansion), which causes it to expand and do work on the piston. Then, the gas is allowed to expand further without gaining or losing heat (adiabatic expansion), which leads to a decrease in temperature. Next, the gas is cooled at a constant temperature (isothermal compression), causing it to contract and do work on the surroundings. Finally, the gas is compressed further without gaining or losing heat (adiabatic compression), resulting in an increase in temperature and returning the gas to its original state.

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

The efficiency of the Carnot Cycle is defined as the ratio of the work output to the heat input. It is given by the equation efficiency = 1 - (Tc/Th), where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir. The Carnot Cycle is considered to be the most efficient thermodynamic cycle, with an efficiency of 100% only achievable in the theoretical case of reversible processes and infinite reservoirs.

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

The Carnot Cycle is used as a benchmark for comparing the efficiency of real-life heat engines, such as steam engines and gas turbines. It is also used in the design of refrigeration and heat pump systems, which use the reverse Carnot Cycle to transfer heat from a cooler environment to a warmer one. The theoretical principles of the Carnot Cycle are also important in the study of thermodynamics and energy conversion.

## 5. What are the limitations of the Carnot Cycle?

The Carnot Cycle is an idealized model that does not take into account factors such as friction and heat losses, which are present in real-life systems. It also assumes that the processes are reversible and that the temperature of the reservoirs remains constant throughout the cycle. These assumptions make the Carnot Cycle a theoretical concept rather than a practical one. Additionally, it is not feasible to achieve 100% efficiency in real systems, as it would require infinite reservoirs and reversible processes.

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