Heat Transfer

An engine relies on the fact that heat is transferred naturally from a higher-temperature region to a lower-temperature region. Even devices designed to cool, such as refrigerators and air conditioners, rely on this principle.

Heat is not transferred naturally in the other direction.

A Heat Engine

A heat engine is a device that uses heat to do work. The gasoline-powered car engine is a good example. In the car engine there are several cylinders. In each cylinder a gas is confined by a piston.

To be useful, the engine must go through cycles, with a certain amount of work being done every cycle. A critical component of any heat engine is that two temperatures are involved. The higher temperature causes the system to expand, doing work, and the lower temperature re-sets the engine so another cycle can begin.

In a full cycle of a heat engine, three things happen:

Heat Q_H is added at a relatively high temperature T_H.
Some of the energy from the input heat is used to do work W.
The rest of the energy is removed as heat Q_L at a relatively low temperature T_L.

This is really a statement of conservation of energy:

|Q_H| = W + |Q_L|

Efficiency

The efficiency of an engine tells you how much of the input energy ends up doing useful work. The efficiency can be stated as a fraction or as a percentage:
e =
W

|Q_H|
=
|Q_H| - |Q_L|

|Q_H|
= 1 -
|Q_L|

|Q_H|

This is the maximum possible efficiency of an engine. In practice losses from friction and other sources reduce the efficiency.

An Ideal (Carnot) Engine

An engine achieves maximum efficiency when it uses reversible processes.

Carnot's Principle: The efficiency of an engine using irreversible processes can be no greater than the efficiency of an engine using reversible processes that is working between the same temperatures. This is named for Sadi Carnot, a French engineer.

Carnot showed that for an ideal (or Carnot) engine, operating between temperatures T_H and T_L, the efficiency is:
e_c = 1 -
T_L

T_H

The efficiency is maximized when the lower temperature is as low as possible, and the higher temperature is as high as possible.
Comparing this to our previous result: e = 1 -
|Q_L|

|Q_H|

For an ideal (Carnot) engine:
|Q_L|

|Q_H|
=
T_L

T_H

P-V Diagram for the Carnot engine

We can derive Carnot's result if we know a little more about the cycle in a Carnot engine. It involves four steps:

Step Description Heat ΔS

1 Isothermal Expansion
at T_H Q_H
ΔS₁ = +
|Q_H|

T_H

2 Adiabatic Expansion
to T_L 0 0

3 Isothermal Compression
at T_L Q_L
ΔS₃ = -
|Q_L|

T_L

4 Adiabatic Compression
to T_H 0 0

Full Cycle - |Q_H| - |Q_L| 0

After completing a cycle the system returns to its original state - the original pressure , volume, temperature, and entropy. If the entropy is the same the total ΔS for the cycle is zero.
ΔS₁ + ΔS₃ =
|Q_H|

T_H
-
|Q_L|

T_L
= 0

Therefore:
|Q_H|

T_H
=
|Q_L|

T_L

This is Carnot's result.

The Third Law of Thermodynamics

The Third Law of Thermodynamics states that it is impossible to reach absolute zero. This means that it is impossible to construct an engine that is 100% efficient - this is why perpetual motion machines are not possible.

Summary of the three laws of thermodynamics

You can't win.
You can't break even.
You can't even get out of the game.