# Carnot engine rejected heat problem

• Nimbalo
In summary, the Carnot engine rejected heat problem is a theoretical concept in thermodynamics that describes the amount of heat energy lost during the operation of a Carnot engine. It is calculated by subtracting the converted heat energy from the total supplied heat energy. The amount of rejected heat is affected by temperature difference, engine efficiency, and working fluid. The Carnot efficiency cannot be improved but engineers can design more efficient engines to reduce the rejected heat. The rejected heat significantly impacts the overall performance of a Carnot engine, with a higher amount resulting in lower efficiency. Reducing rejected heat is a crucial goal in thermodynamic engineering.
Nimbalo

## Homework Statement

From the hot reservoir at a temperature of T1, Carnot Engine A takes an input heat of 5550J, delivers 1750J of work and rejects heat to a cold reservoir that has a temperature of 503K. This cold reservoir also serves as the hot reservoir for a second Carnot Engine, B, which uses the rejected heat from the first engine as input heat. Engine B also delivers 1750J of work, while rejecting heat to an even colder reservoir that has a temperature T2. Find T1 and T2.

e=1-Tc/Th
e=W/Qh

## The Attempt at a Solution

I plugged in my values into the e=1-Tc/Th and e=W/Qh equations to solve for the Th, or T1. As an answer, I got 734.3K. However, I'm missing a variable for my second Carnot engine. What is the input heat for engine B? I tried doing 734.3-503K, but that gives me answers in K and makes the equation not work. I don't know what I'm supposed to use for the input heat.

Welcome to PF

Nimbalo said:
What is the input heat for engine B?

It's the same as the output heat from engine A:
... a second Carnot Engine, B, which uses the rejected heat from the first engine as input heat.

Engine A has 5550 J of input heat. Of that 5550 J energy, 1750 J is used to do work. The remaining energy has to go somewhere (conservation of energy) ...

so what does this mean? what do i do with the conservation of energy?

copitlory8 said:
what do i do with the conservation of energy?
Equate the input energy with the total output energy.
Qin = W + Qout
If you need more help with the problem, you will have to show how far you have gotten and the work you have done.

I would first clarify with the person or group who provided the problem whether they intended for the input heat for Engine B to be the rejected heat from Engine A, or if there is additional input heat from an external source. If the intention is for Engine B to only use the rejected heat from Engine A, then the input heat for Engine B would be 1750J. However, if there is additional input heat from an external source, then that value would need to be provided in order to solve for T2.

Additionally, I would also check the units of the given temperatures and make sure they are consistent with the units used in the Carnot efficiency equations. If they are not consistent, then the temperatures would need to be converted to the appropriate units before solving the equations.

## 1. What is the Carnot engine rejected heat problem?

The Carnot engine rejected heat problem is a theoretical concept in thermodynamics that describes the amount of heat energy that is lost or wasted during the operation of a Carnot engine. It is based on the second law of thermodynamics, which states that heat will always flow from a hotter object to a cooler object, and that it is impossible to create a perfect engine that converts all heat energy into work.

## 2. How is the rejected heat calculated in a Carnot engine?

The rejected heat in a Carnot engine is calculated by subtracting the amount of heat energy that is converted into work from the total amount of heat energy that is supplied to the engine. This is known as the Carnot efficiency, and it can be calculated using the formula Qc/Qh = 1 - Tc/Th, where Qc is the rejected heat, Qh is the heat input, Tc is the temperature of the cold reservoir, and Th is the temperature of the hot reservoir.

## 3. What factors affect the amount of rejected heat in a Carnot engine?

The amount of rejected heat in a Carnot engine is affected by several factors, including the temperature difference between the hot and cold reservoirs, the efficiency of the engine, and the type of working fluid used. Generally, a larger temperature difference and a more efficient engine will result in a smaller amount of rejected heat.

## 4. Can the Carnot efficiency be improved to reduce the amount of rejected heat?

No, the Carnot efficiency is based on the second law of thermodynamics and cannot be improved. However, engineers can design more efficient engines that come closer to the Carnot efficiency, resulting in a smaller amount of rejected heat. This is why the Carnot engine is considered a theoretical ideal and not a practical engine.

## 5. How does the rejected heat impact the overall performance of a Carnot engine?

The rejected heat plays a significant role in the overall performance of a Carnot engine. The higher the amount of rejected heat, the lower the efficiency of the engine will be, as less heat energy is converted into work. This is why reducing the amount of rejected heat is a crucial goal in thermodynamic engineering.

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