Heat Engine and Carnot Engine

Heat Engine

Any device which converts heat energy continuously into mechanical work is called a heat engine. The main parts of heat engines are:

1. Source: The source is a hot body at a constant high temperature from which the heat engine can draw heat.
2. Sink: Sink is a cold body at a constant low temperature to which any amount of heat can be rejected.
3. Working substance: Working substance is an ideal gas which on being supplied with heat performs mechanical work.

Efficiency of Heat Engine
It is defined as the ratio of the external work obtained to the heat energy absorbed by the working substance from the source. It is denoted by η.

$$ \eta = \frac {\text {external work obtained}} {\text {heat energy absorbed from the source }} $$

Figure shows the block diagram of a heat engine. Let Q₁ be the amount of heat absorbed by the working substance from the source at higher temperature T₁, W be the mechanical work done by the working substance, and Q₂ be the remaining part of heat rejected to sink at lower temperature, T₂. Therefore, (Q₁ – Q₂) is the amount of heat converted into the mechanical work.

\begin{align*} \therefore W &= Q_1 – Q_2 \\ \text {The efficiency of the engine,} \eta = \frac {W}{Q_1} &= \frac {Q_1 – Q_2}{Q_1} \\ &= 1 - \frac {Q_2}{Q_1} \\ \end{align*}

No engine will convert all the heat absorbed from the source into work. So, the efficiency of an engine is always less than one or 100%.

Second Law of Thermodynamics

The second law of thermodynamics can be stated in different ways. This law has been stated in a number of ways but all the statements are logically equivalent to one another which are stated later.

Kelvin Plank Statement

It is impossible for an engine to convert all the heat energy into work without rejecting some energy to sink i.e. no engine will have 100% efficiency.

This statement is applicable for heat engines. In heat engine, the working substance absorbs some heat from the source (at higher temperature), converts a part of heat into mechanical work and rejects the remaining part to the sink (at lower temperature). Therefore, the presence of sink is essential for the continuous conversion of heat into work. We cannot obtain the continuous conversion of heat into work. We cannot obtain the continuous supply of work from a single body i.e. the source of heat alone.

Clausius Statement

It is impossible to absorb heat energy from cold body and reject to a hot body without doing work ie. Self-acting refrigerator is impossible.

In refrigerator working substance takes in heat from a cold body, a certain amount of work is done on it by some outside agency and rejects a larger amount of heat to a hotter body. Therefore, refrigerator transfers heat from a cold body to a hot body with the aid of an outside agency.

Carnot Engine

Carnot devised an ideal cycle of operation for a heat engine in 1824. This cycle is known as Carnot cycle. The machine used for realizing this ideal cycle of operation is called an ideal heat engine or Carnot heat engine. The essential parts of an ideal heat engine or Carnot heat engine are shown in figure.

• Source of heat
  A hot body infinite thermal capacity is a source of heat. The source is maintained at a fixed higher temperature T₁ from which the working substance draws heat without changing its temperature.
• Cylinder
  A cylinder fitted with a perfectly non-conducting and frictionless piston enclosing an ideal gas. The bottom of the cylinder is a perfect heat conductor whereas the walls are perfect heat insulator.
• Sink of heat
  The sink should be at a fixed lower temperature, T₂ to which any amount of heat can be rejected. It also has finite thermal capacity and its temperature remains at T₂.
• Working substance
  An ideal gas acts as the working substance filled in a cylinder with mom-conducting sides but perfectly conducting base. Apart from these essential parts, there is a perfectly insulating stand on which the cylinder can be placed. It would completely isolate the working substance from the surroundings.

The working substance is subjected to a cycle of four operations consists of two isothermal processes and two adiabatic processes as shown in figure. Such a cycle is known as Carnot’s cycle.