Heat Engine

A heat engine is designed to convert thermal energy into mechanical work through a cyclic process. It operates according to the principles of thermodynamics, which regulate energy transformations and Efficiency. Heat engines are crucial for converting thermal energy into mechanical work, impacting transportation, energy production, and industrial processes. Understanding their principles, types, and Efficiency helps optimize their performance and advance technology.

1.0Definition of Heat Engine

Heat engines operate based on the principle that energy can be transformed from one form to another. In a heat engine, thermal energy (heat) is converted into mechanical energy (work) through a series of thermodynamic processes, typically involving heat absorption, work extraction, and heat rejection.

2.0Heat Engine Diagram

3.0Explanation of Heat Engine

Heat Engine has the following Essential parts

1. Source-It is a heat reservoir at a high-temperature T_1 and is assumed to have an infinite thermal capacity, meaning that any heat can be extracted without affecting its temperature.
2. Sink-It is a cold reservoir at a lower temperature T_2 and has an infinite thermal capacity, allowing any amount of heat to be added without altering its temperature.
3. Working Substance-A Working substance is any material (solid, liquid, or gas) that performs mechanical work when heat is supplied. For example, a mixture of fuel vapour and air is used in a gasoline or diesel engine or steam in a steam engine.

4.0Working of Heat Engine

In each operational cycle, the working substance of the heat engine absorbs a specific quantity of heat Q_1 from a high-temperature source at T_1. It converts a portion of this heat energy into mechanical work W ,while the remaining heat Q_2 is expelled to a lower-temperature sink at T_2. The mechanical work W performed during the cycle is then transferred to the environment through a mechanism, such as a piston within a cylinder that delivers energy to the wheels of a vehicle via a shaft.

5.0Heat Engine P-V Diagram

6.0Types of Heat Engines

Heat engines come in several different types, each with its own operating principles and applications. Here are some of the primary varieties:

1. Carnot Engine

• Description: An idealized engine functioning on the Carnot cycle operates through four stages: two isothermal processes (for heat absorption and rejection) and two adiabatic processes (for expansion and compression).
• Principle: This principle Provides the theoretical maximum efficiency limit for heat engines. It helps in understanding the fundamental limits of converting heat into work.
• Applications: Primarily used for theoretical analysis and setting benchmarks for real engines.

2. Otto Engine

• Description: A type of internal combustion engine that operates on the Otto cycle, which includes intake, compression , power, and exhaust strokes.
• Principle: The engine compresses a fuel-air mixture and ignites it with a spark, causing combustion that drives the piston.
• Applications: Widely used in gasoline-powered vehicles such as cars and motorcycles.

3. Diesel Engine

• Description: Another type of internal combustion engine, but it operates on the Diesel cycle, where air is compressed to a high temperature and pressure before fuel injection.
• Principle: The fuel is injected into the high-pressure, high-temperature air, causing spontaneous ignition. This process is more efficient than the Otto cycle.
• Applications: Common in trucks, buses, and industrial machinery due to its fuel efficiency and durability.

4. Gas Turbine Engine

• Description: Also known as a jet engine, it operates on the Brayton cycle, involving continuous intake, compression, combustion, and exhaust.
• Principle: Air is compressed, mixed with fuel, burned, and then expanded to produce thrust or mechanical power.
• Applications: Used in aircraft for propulsion, and in power plants for electricity generation.

7.0Heat Engine Efficiency

• The Efficiency of a heat engine is defined as the ratio of the engine's net work output per cycle to the heat absorbed by the working substance from the heat source.
• As the working substance returns to its initial state after completing one cycle, its internal energy does not change.
• By the First Law of Thermodynamics

The net heat absorbed during a cycle is equal to the work done by the engine.

$Q_1-Q_2=\mathrm{W}$

• Efficiency of heat engine $(\eta )=\frac{\text{ Work done by engine }(\text{ output })}{\text{ Heat absorbed from the source(input) }}$
• $\eta =\frac{W}{Q_1}=\frac{Q_1-Q_2}{Q_1}=1-\frac{Q_2}{Q_1}$
• The efficiency of a heat engine is always less than one , when Q2=0,=1 or 100%,but any working substance in a cycle cannot convert all the heat extracted from the source into work.It has to reject some amount of heat into the sink.That is why the efficiency of a heat engine is always less than unity. 
• The efficiency of a steam engine varies from 12 to 16%.The maximum efficiency of a petrol engine is 26%, and that of a diesel engine is 40%.

8.0Heat Engine Applications

1. Transportation

• Automobiles: Internal combustion engines (ICEs), such as those operating on the Otto and Diesel cycles, power cars, motorcycles, and trucks. They convert fuel energy into mechanical work to drive vehicles.

2. Power Generation

• Steam Power Plants:  Rankine cycle engines, which employ Steam turbines, are frequently employed in power plants to generate electricity. These engines convert heat from burning fossil fuels or nuclear reactions into electrical energy.

3.  Heating and Cooling

• Heat Pumps: Though not engines in the traditional sense, heat pumps operate on similar principles. 

9.0Sample Questions on Heat Engine

Q-1.  Is the Efficiency of a heat engine higher in hilly areas than in the plains?

Solution:

In hilly areas ,the temperature of the surroundings is lower than that in plains, so the ratio $\frac{T_2}{T_1}$ is less in hilly areas than that in plains 

$\eta =1-\frac{T_2}{T_1}$

Hence Efficiency is higher in hilly areas than in plains.

Q-2. A steam engine delivers $5.4\times 10^8\mathrm{J}$ of work per minute and consume

$3.6\times 10^9\mathrm{J}$ of heat per minute from its boiler. What is the efficiency of the engine? How much heat is wasted per minute?

Solution:

Work output =$5.4\times 10^8\mathrm{J}$

Heat Input =$3.6\times 10^9\mathrm{J}$

Efficiency,

$\eta =\frac{W}{Q_1}=\frac{5.4\times 10^8}{3.6\times 10^9}=0.15=15\%$

Heat wasted Per Minute

$Q_2=Q_1-W=3.6\times 10^9-5.4\times 10^8=3.1\times 10^9\mathrm{J}$

Q-3. What is the efficiency of an ideal heat engine that operates between the freezing and boiling points of water?

Solution:

Efficiency of Ideal Heat Engine,

$\eta =\left(1-\frac{T_2}{T_1}\right)\times 100$

$\eta =\left(1-\frac{273}{373}\right)\times 100=26.8\%$

Q-4. A reversible engine converts one-fifth of the heat from the source into work. When the sink's temperature decreases by 70° , its efficiency is doubled. Determine the temperatures of the source and the sink.

 Solution:

$W=\frac{1}{5}{Q}_1$

$Q_2=Q_1-W=Q_1-\frac{1}{5}{Q}_1=\frac{4}{5}{Q}_1$

$\frac{Q_2}{Q_1}=\frac{4}{5}=\frac{T_2}{T_1}$ ………..(1)

Efficiency

$(\eta )=1-\frac{T_2}{T_1}=1-\frac{4}{5}=\frac{1}{5}$

On reducing the temperature of the sink by 70⁰, the efficiency is doubled

$\left(\therefore 2\eta =1-\frac{\left(T_2-70\right)}{T_1}\right)$

$2\times \frac{1}{5}=1-\frac{T_2}{T_1}+\frac{70}{T_1}=1-\frac{4}{5}+\frac{70}{T_1}$

$\frac{2}{5}=\frac{1}{5}+\frac{70}{T_1}\Rightarrow T_1=350\mathrm{K}$

$T_2=\frac{4}{5}{T}_1=\frac{4}{5}\times 350=280\mathrm{K}$