Heat Engine and Heat Pumps

Heat Engine:

What is Heat Engine?

Heat engine is a device by which a system is made to undergo a cyclic process that results in conversion of heat to work. It consists of a working substance called the system.

Example: A mixture of fuel vapour and air in a gasoline or diesel engine or steam in a steam engine are the working substances.

Working of Heat Engine:

The working substance goes through a cycle consisting of several processes. In some of these processes, it absorbs a total amount of heat Q₁ from an external reservoir at some high temperature T₁. In some other processes of the cycle, the working substance releases a total amount of heat Q₂ to an external reservoir at some lower temperature T₂. The work done (W) by the system in a cycle is transferred to the environment via some arrangement (e.g. the working substance may be in a cylinder with a moving piston that transfers mechanical energy to the wheels of a vehicle via a shaft). The cycle is repeated again and again to get useful work for some purpose. The discipline of thermodynamics has its roots in the study of heat engines.

Heat Engine

The efficiency (h) of a heat engine is defined by,

h = ------ (1)

Where Q₁ is the heat input i.e., the heat absorbed by the system in one complete cycle and W is the work done on the environment in a cycle. In a cycle, a certain amount of heat (Q₂) may also be rejected to the environment. Then, according to the First Law of Thermodynamics, over one complete cycle,

W = Q₁ – Q₂ ------ (2)

i.e., h = 1 − ------ (3)

For Q₂ = 0, h = 1, i.e., the engine will have 100% efficiency in converting heat into work.

Note that the First Law of Thermodynamics i.e., the energy conservation law does not rule out such an engine. But experience shows that such an ideal engine with h = 1 is never possible, even if we can eliminate various kinds of losses associated with actual heat engines. It turns out that there is a fundamental limit on the efficiency of a heat engine set by an independent principle of nature, called the Second Law of Thermodynamics. The mechanism of conversion of heat into work varies for different heat engines. There are two ways: the system (say a gas or a mixture of gases) is heated by an external furnace, as in a steam engine; or it is heated internally by an exothermic chemical reaction as in an internal combustion engine. The various steps involved in a cycle also differ from one engine to another.

Types of Heat Engine:

Steam engine:

• Internal combustion engine

• Gas turbine

There are three main parts in an engine.  A hot body called source, a working substance, and a body called sink. There must be the source of heat of infinite thermal capacity, and that should be at a constant high temperature so that if any amount of heat is withdrawn from it or given to it, that does not affect its temperature. It must be some substance through which the heat is absorbed or rejected into the sink .This is the working substance. There must be a sink of finite thermal capacity, and that should be at a constant high temperature so that if any amount of heat is withdrawn from it or given to it, that does not affect its temperature.

Carnot Engine:

Carnot designed a theoretical engine. This engine cannot be realized in actual practice.

Carnot cycle:

The working substance of the engine undergoes a cycle known as Carnot cycle. It consists of the following four strokes.

I. Isothermal expansion.

II. Adiabatic expansion.

III. Isothermal compression.

IV. Adiabatic compression.

Carnot Engine

Efficiency of Carnot Cycle:

η =

=

η =1−

Where T₁ and T₂ are in Kelvin.

1. Efficiency of a heat engine depends only on temperatures.

2. Efficiency of a heat engine is always lesser than unity, i.e., whole of heat can never be converted into work which is in accordance with second law.

Carnot Theorem:

Carnot’s reversible engine working between two given temperature is considered to be the most efficient engine.

Refrigerator and Heat pump:

A refrigerator is the reverse of a heat engine. Here the working substance extracts heat Q₂ from the cold reservoir at temperature T₂, some external work W is done on it and heat Q₁ is released to the hot reservoir at temperature T₁.

Example: Most commonly used refrigerant in heat pump is Chlorofluorocarbons

Compressor and Decompressor

A heat pump is the same as a refrigerator. If the purpose is to cool a portion of space, like the inside of a chamber, and higher temperature reservoir is surrounding the device, a refrigerator, if the idea is to pump heat into a portion of space (the room in a building when the outside environment is cold), the device is called a heat pump.

In a refrigerator the working substance (usually, in gaseous form) goes through the following steps:

1. Sudden expansion of the gas from high to low pressure which cools it and converts it into a vapour-liquid mixture,

2. Absorption by the cold fluid of heat from the region to be cooled converting it into vapour,

3. Heating up of the vapour due to external work done on the system,

4. Release of heat by the vapour to the surroundings, bringing it to the initial state and completing the cycle.

The coefficient of performance (a) of a refrigerator is given by

a = ------ (1)

Where Q₂ is the heat extracted from the cold reservoir and W is the work done on the system–the refrigerant. (a for heat pump is defined as )

Note that while h by definition can never exceed 1, a can be greater than 1. By energy conservation, the heat released to the hot reservoir is,

Q₁ = W + Q₂

i.e., a = ------ (2)

In a heat engine, heat cannot be fully converted to work; likewise a refrigerator cannot work without some external work done on the system, i.e., the coefficient of performance in Eq. (1) cannot be infinite.

Carnot Refrigerator:

· For Carnot refrigerator = =

· Coefficient of performance β =

where

= temperature of surrounding

= temperature of cold body

Relation between coefficient of performance and efficiency of refrigerator is,

β =

Purpose and Advantage of Heat Pump:

• The purpose of a heat pump is to transfer energy to a warm environment, such as a home in the winter.

• The great advantage of using a heat pump to keep your home warm rather than just burning fuel in a fireplace or furnace is that a heat pump supplies. It runs on electricity, so you can save substantially on fuel consumption.

• Heat pump warms air from one place to another, to where it is needed depending on the season.

• Even in the air that seems too cold, heat energy is present.

• When it’s cold outside, a heat pump extracts this outside heat and transfers it inside.

• When it’s warm outside, it reverses directions and acts like an air conditioner, removing heat from your home.

Disadvantage of Heat Pump:

The disadvantage of a heat pump is that the work input is sometimes more expensive than simply burning fuel, especially if the work is provided by electrical energy.