Heat Engine Efficiency

What is Heat Engine?

A heat engine is a device that converts heat to work. It takes heat from a reservoir then does some work like moving a piston, lifting weight etc, and finally discharging some of the heat energy into the sink. Schematically it can be represented as:

Heat Engine - Engine Efficiency

Heat Engine Efficiency

Let us derive an expression for the efficiency of a heat engine. We can define heat engine efficiency as:

\(η\) =\({W}{Q_1}\)

Where,

\(W \)= Work done by the engine

\(Q_1\) = Heat taken from the source

After each cycle, the engine returns to its initial state so,

\(∆U\) =\( 0\).

So from the figure it is clear that,

\(W\) = \(Q_1- Q_2\)

Hence the heat engine efficiency is:

\(η\) =\(\frac{Q_1- Q_2}{Q_1}\)

\(η \) = \(1- \frac{Q_2}{Q_1}\)

So for \(Q_2\) = \(0\), efficiency will be 100% but in actual this is not possible because there will be some loss of energy in the system. Hence for every engine there is a limit for its efficiency. It has been found that efficiency is maximum for a reversible engine like Carnot heat engine.

Following is the table explaining related concepts of heat engine:

Heat Pump:

So now that we have seen the above system we will now see what a refrigerator is. Before getting into the working of refrigerator we will define Heat pump. It is a device used to pump heat into the system. So it is similar to a refrigerator but works exactly opposite to it. A refrigerator takes out heat from a lower temperature \(T_2\) and releases it to a higher temperature \(T_1\). For this process to happen some work is done on the system. It can be schematically represented as follows:

Heat Engine

In this case, we define the coefficient of performance. It is defined as:

\(α\) = \(\frac{Q_2}{W}\)

Where, \(Q_2 \)= Heat taken from the system

W = Work done on the refrigerator

Similar to heat engine after a cycle the refrigerator returns to its original state hence ∆U = 0. So from the figure,

\(W\) = \(Q_1 – Q_2\)

Therefore,

\(α \)=\(\frac{Q_2}{Q_1 – Q_2}\)

A refrigerator will not be able to function without external work so its coefficient of performance can never be infinite.

Below video will help you visualize and understand the concept of transition of heat.


Going further we will see what second law of thermodynamics is and how Carnot heat engine is the most efficient engine. To explore more on heat engines, download BYJU’S – The Learning App.

Heat Engine Questions

Q1) What is a heat engine?

Answer:

A heat engine is a device that converts heat to work.

Q2) Which of the following type of work does a heat engine convert heat energy from fuel combustion or any other source?

  1. Mechanical work
  2. Pressure work
  3. Electrical work
  4. None of the above

Answer: a. Mechanical energy

Heat engine gives mechanical energy as an output.

Q3) The formula to find the heat efficiency is _____.

  1. \(\eta =1-\frac{Q_2}{Q_1}\)
  2. \(\eta =\frac{Q_1}{Q_2}-1\)
  3. \(\eta =\frac{Q_1-Q_2}{Q_1}\)
  4. \(\eta -1=\frac{Q_1}{Q_1-Q_2}\)

Answer: a. \(\eta =1-\frac{Q_2}{Q_1}\)

The formula to find the heat efficiency is \(\eta =1-\frac{Q_2}{Q_1}\).

Q4) What is a heat pump?

Answer:

A heat pump is a device that transfers heat from colder region to hotter region using mechanical energy.

Q5) List a few differences between the heat pump and refrigerator.

Answer:

Heat Pump

Refrigerator

Heat is withdrawn from the environment

Heat is withdrawn from the inside of the refrigerator

The temperature inside the fridge drops

A negligible temperature drop in the environment

The heat extracted is given off to the building

The heat extracted is given off to the environment

Q6) Which of the following is true of a heat pump?

  1. A heat pump removes heat from the building to achieve cooling
  2. Heat pump supplies heat at high temperature
  3. Both of the above
  4. None of the above

Answer: b. Heat pump supplies heat at high temperature

Q7) Which of the following is a power absorbing heat engine?

  1. Air compressor
  2. Petrol Engine
  3. Steam Engine
  4. None of the above

Answer: Air compressor

Air compressor is a power absorbing heat engine.

Q8) A steam engine comes under the category of _____.

  1. Internal combustion engine
  2. External combustion engine
  3. All of the above
  4. None of the above

Answer: b. External combustion engine

A steam engine comes under the category of the external combustion engine.


Practise This Question

The Young's modulus of a wire of length  L and radius r is  Y N/m. If the length and radius are reduced to L2 and r2, then its Young's modulus will be