### VI. The Second Law of Thermodynamics

To summarize the previous page,
1. For heat to flow from a source to a sink, there must be a temperature difference.
2. When heat is transferred from one body to another, the temperatures equalize. As the temperature of the heat source falls, that of the heat sink rises.
3. When temperatures are equal, no more heat can be transferred, even though the hot and cold objects still contain heat.
4. When heat is converted into work, the temperature of the heat source falls, approaching that of the heat sink.
5. If there is no temperature difference, no heat can be converted into work. But if there is a temperature difference, some of the heat will be used to raise the temperature of the heat sink.
6. If some of the heat must go into raising the temperature of a sink, not all of it can be converted into work.
7. Therefore,
 It is not possible to construct an engine which does nothing but convert heat into useful work.

or more generally,

 It is not possible to convert one form of energy to another with 100% efficiency.

The only exception is that 100% of any useful energy can be dissipated as waste heat.

This has important consequences for how we use energy. Normally it is always better to use energy with as few changes of form as possible; so that it is, in principle, better to use the rotary motion of an internal combustion engine to drive a car's wheels than to use the same engine to drive a generator, then use the electricity to drive the car's wheels.

However, in practical engineering we sometimes find that it is better to use a device as a secondary source of energy than as a primary source. For example, one of the simplest hybrid automobile designs does what we just said was the wrong thing to do: it uses an internal combustion engine to drive a generator which stores electricity in batteries, then turns the wheels with electric motors. BUT it turns out that real automobiles do not normally operate at the most efficient engine rate because the engine is coupled to the wheels. Decoupling from the drive train allows the engine to always function at optimum, more than making up for the energy losses incurred by converting rotary motion into electricity, then back into rotary motion.

The Second Law of Thermodynamics can be stated in several ways:

• It is not possible to convert one form of energy to another with 100% efficiency.

• Heat will not flow spontaneously from a cold body to a hot body. (This is from your text.)
Refrigerators and air conditioners use mechanical work to move heat against its natural preference, that is, from a cold place to a warmer place. See the reserve articles and this page from How Stuff Works.
• Every isolated system becomes more disordered with time. This is NOT a statement of the Second Law, but a metaphor; see Prof. Lambert's site on the Second Law.

• The entropy of an isolated system remains constant or increases. This is a verbal statement of the most precise, mathematical form of the law. Unfortunately, entropy is something for which it is difficult to give a precise verbal description. See Prof. Lambert's more mathematically detailed site on the Second Law.
Remember, "entropy always increases" only applies to isolated systems. The Earth, and the surface ecosystems of the Earth in particular, are not isolated systems! Individual parts of a system, even an isolated one, can decrease their own entropy at the expense of a larger increase somewhere else within the system.

### Consequences of the Second Law of Thermodynamics include

The Arrow of Time
Time's direction is a direct consequence of the Second Law of Thermodynamics. This is because any process in which entropy increases is irreversible, and we can always tell if a movie of the process is running backwards. How many shattered lightbulbs have you seen spontaneously reassembling -- unless a movie is being run backwards?

Energy use
Energy can never be used with 100% efficiency; some of it must always be dissipated. This is another way of saying that perpetual motion is impossible.

The Heat Death of the Universe
Left to themselves, all things tend to equalize their temperatures. In an isolated system, eventually everything will be the same temperature and heat will no longer be able to flow. But since heat engines or reasonable facsimiles are the only things capable of performing useful work, this means that no part of that isolated system (now isothermal as well) will be able to do work on any other part.

The universe is an isolated system, unless Someone outside intervenes.

 Copyright © 2001 by Daniel J. Berger. This work may be copied without limit if its use is to be for non-profit educational purposes. Such copies may be by any method, present or future. The author requests only that this statement accompany all such copies. All rights to publication for profit are retained by the author.