# Carnot engine efficiency problem

In summary, a Carnot engine absorbed 1.0 kJ of heat at 300 K and exhausted 400 J of heat at the end of the cycle. Using the formula for efficiency, the calculated temperature at the end of the cycle is 120K.

## Homework Statement

A Carnot engine absorbed 1.0 kJ of heat at 300 K, and exhausted 400 J of heat at the end of the cycle. What is the temperature at the end of the cycle?

## Homework Equations

The efficiency of a Carnot engine is given by the formula
Efficiency = 1 – Qc/Qh
= 1 – Tc/Th

## The Attempt at a Solution

Efficiency = 1 – 300J/1000J
= 0.7 = 70%
0.7 = 1 – Tc/Th = 1 – Tc/300K
Tc = 90K
Is it correct? I am trying to self study the topic Carnot cycle for a report

Welcome to PF!

## The Attempt at a Solution

Efficiency = 1 – 300J/1000J
= 0.7 = 70%
0.7 = 1 – Tc/Th = 1 – Tc/300K
Tc = 90K
Is it correct?
Did you mean to use 300 J for QC? The problem statement gives 400 J.

Otherwise, I think your calculation is correct. However, to specify the temperature at the end of the cycle, you need to know which point of the cycle is taken to be the "end of the cycle".

Oh i see i misread the problem so it should be
Efficiency = 1 – 400J/1000J = 0.6
Then
0.6 = 1 – Tc/Th = 1 – Tc/300K
Tc = 120K

OK. I'm still not clear on which point of the cycle is the endpoint. So I'm not sure if TC is the temperature at the endpoint. But your work for TC looks good.

## 1. What is a Carnot engine?

A Carnot engine is a hypothetical engine that operates on the Carnot cycle, a theoretical thermodynamic cycle that represents the most efficient way to convert heat into work. It serves as a model for the maximum possible efficiency of any heat engine.

## 2. How does a Carnot engine work?

A Carnot engine consists of a working substance (such as a gas) contained within a cylinder. The working substance is alternately heated and cooled, causing it to expand and contract, which drives a piston to do work. This process is repeated in a cyclical manner.

## 3. What is the Carnot efficiency formula?

The Carnot efficiency formula is: efficiency = (Th - Tc) / Th, where Th is the temperature of the heat source and Tc is the temperature of the heat sink. This formula represents the maximum possible efficiency for a heat engine operating between two temperature extremes.

## 4. Why is the Carnot engine considered to be the most efficient?

The Carnot engine is considered to be the most efficient because it operates on a theoretical cycle that eliminates all sources of inefficiency, such as friction and heat loss. This means that it represents the maximum possible efficiency that can be achieved by any heat engine.

## 5. What factors affect the efficiency of a Carnot engine?

The efficiency of a Carnot engine is affected by the temperature of the heat source and heat sink, as well as the type of working substance used. It is also influenced by the Carnot cycle itself, which involves reversible processes that minimize energy loss.

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