# Energy, work, heat, and power

## ©2019 L A Waygood

The terms ‘energy‘, ‘work‘, and ‘power‘ are often used interchangeably by the layman and by journalists. And the meaning of  the ‘heat‘ has an ‘everyday’ definition which is quite different from its scientific meaning.

So, let’s try and sort out the confusion between these terms.

### Energy

Energy‘ is one of those unfortunate scientific terms which is defined in terms of what it does, rather than what it is. This is somewhat unsatisfactory, because most of us like to know what something is, not just what it does. Unfortunately, a search of the worldwide web is unlikely to return any understandable explanation of what energy is.

Whatever it is, we know that energy obeys what is known as the ‘Law of the Conservation of Energy‘, which tells us that in any closed system, the total amount of energy is fixed which, in turn, means that energy can be neither created nor destroyed, but can only be transformed from one form into another.

This very important concept is brilliantly-explained, in terms of a child’s toy building blocks, in the text of a lesson on energy by the American Nobel prizewinner and lecturer, Dr Robert Feynman.

In this lecture, Dr Feynman, concludes that, while we can use numerous formulae for calculating some numerical quantity ( a figure) for energy, we have no knowledge of what energy actually is!

So if, for example, we were to raise a weight through a particular vertical distance, and we then multiplied that weight by the vertical distance through which it moved, then we end up with a figure which, for convenience, we call the ‘potential energy’ of that weight.

This figure, which we have called ‘potential difference’, is an abstract thing. It’s not some sort of ‘stuff’ which we can describe, or see, or touch, or smell but, rather, a figure which, no matter what process it goes through always remains the same. For example, if we were to allow that same weight to fall to the ground, then that figure we called ‘potential energy’ would disappear, only to then re-appear as exactly the same figure which, for convenience, this time, we call ‘kinetic energy’.

The ‘numerous formulae’ (such as those for potential and kinetic energy, etc.) that we referred to in an earlier paragraph, are based on the assumption that energy, this ‘abstract thing’ or ‘figure’, can be categorised as either potential energy or kinetic energy. ‘Potential energy’ exists by virtue of an object’s position, whereas ‘kinetic energy’ exists by virtue of an object’s movement. All other ‘forms’ of energy, electrical, chemical, etc., are simply sub-categories of potential or kinetic energy.

So, because we cannot explain what energy is, we must satisfy ourselves with understanding what energy does.

For that reason, we simply define energy as: ‘the rate of doing work’.

But, even this definition is unsatisfactory, because it does rather assume everyone knows what is meant by ‘work’!

### Work

Now, work is generally defined as force multiplied by the distance moved in the direction of that force. But this is a rather difficult concept to apply to electricity, so a far better definition, and one which is far easier to understand, is one commonly used in thermodynamics, which states that ‘work describes the conversion of energy from one form into another’.

So, for example, when a generator converts kinetic energy into electric energy, that generator is doing work. And, when an electric motor converts electrical energy into kinetic energy, then that motor is doing work.

So, scientists describe work as energy in transit‘ between one form and another.

### Heat

In thermodynamics, heat is defined as ‘the transfer of energy from a warmer body to a cooler body’.

So, scientists also describe heat as energy in transitbut, this time, from a warmer body to a cooler body’.

### Units of measurement for energy, work, and heat

In SI, the unit of measurement for energy is the joule (symbol: J), named in honour of the English physicist, James Prescott Joule.

Because both work and heat both describe ‘energy in transit’, they each share the same SI unit of measurement: the joule (symbol: J).

The joule represents a very small quantity of energy so, for the purpose of billing their customers, energy companies measure the energy that they supply in an alternative, much larger unit, called the kilowatt hour (symbol: kW·h), which is equivalent to 3 600 000 J (3.6 MJ). While the kilowatt hour is a metric unit, it is not an SI unit.

### Power

Power is simply the rate at which energy is transferred. As energy can either be transferred from one form into another, or from a warmer body to a cooler body, then we can define power as either:

Power is ‘the rate of doing work’, or ‘the rate of heat transfer’.

So ‘power‘ is nothing more than a rate‘; again, it’s not some sort of ‘stuff’ we can see, touch, or smell. So we cannot ‘transfer power’, ‘use power’, ‘expend power’; it’s simply the rate at which we ‘transfer energy’, ‘use energy’, or ‘expend energy’.

As it’s a rate, then the SI unit of power is the joule per second (symbol: J/s) but, as in common with some other SI derived units (like the volt, coulomb, etc.), this is given a special name, the ‘watt‘ (symbol: W).

In North America, it’s common for the output power of an electric motor* to be expressed in horsepower, which is the Imperial Unit for power. This has, unfortunately, led to the widespread belief that ‘electrical power’ is measured in watts, whereas ‘mechanical power’ is measured in horsepower. In fact, there is no such thing as ‘electrical’ or ‘mechanical’ (or any other form!) of power, as power is simply nothing more than a ‘rate’.

(*Elsewhere, both the input and output power of a motor are expressed in watts.)

So, the watt and the horsepower are simply two different units for measuring exactly the same quantity! Accordingly, it would be equally correct, if you wished, to express the power of, say, an electric lamp or an electric heater in horsepower, or the output of a steam engine in kilowatts!

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