Types of Energy and the units used to measure it

Many branches of science and technology are involved with energy, and each group originally defined energy using units that they considered useful. It was only much later that these different forms of energy were recognized as different manifestations of the same fundamental quantity. However, the multiplicity of units remains and can be a source of confusion.

One common source of confusion is the difference between mass and weight. Although the two are often used interchangeably, they are fundamentally different quantities. Mass, usually denoted by the letter m, refers to a quantity of matter and is measured in kilograms in the metric system. Weight is the pull of gravity on a mass, and is usually denoted by the symbol w. It is measured in pounds in the British system and Newtons in the Metric system. The two are simply related near the surface of the Earth: to convert mass to weight, you must multiply by the acceleration of gravity, which equals 9.8 m/s2 in the metric system. Thus a mass of m kilograms has a weight of 9.8m Newtons. Note that a body far from the earth may be “weightless,” since the pull of the earth is negligibly small, but its mass has not changed at all from its value at the surface.

1. Units of work and energy

Originally, people thought of two different kinds of energy: mechanical energy associated with exerting forces on physical objects and heat energy, which was associated with heating and cooling.  Each group of people defined units that were considered to be useful in these different domains.

Mechanical energy is defined as the work done by a force acting through a distance, and is measured in foot-pounds or Newton-meters, which are called joules. A foot-pound is the work done when a force of 1 pound acts through a distance of 1 foot, and the Newton-meter (or joule) was defined in a similar way. No mechanical work is done if the force does not move the body. Standing still may be tiring, but no physical work is done.

Heat energy is defined as the energy absorbed or released when an object is heated or cooled. Specifically, a calorie (lower-case c) is the energy needed to change the temperature of 1 gram of water by 1 degree Celsius, and a British Thermal Unit (BTU) is the energy needed to change the temperature of 1 pound of water by 1 degree Fahrenheit. A Calorie (upper-case C) is 1000 times the size of a calorie (lower-case c), and so is the energy needed to change the temperature of 1000 grams (or 1 kilogram) of water by 1 degree Celsius. The energy content of foods is often indicated in Calories. European food wrappers often use kJ for kilojoules (1000 joules) instead of Calories.

There are many, many other units of energy. For example, air conditioners are often rated in tons, which is an amount of energy needed to melt 1 ton of ice. The origin of the unit is clear – air conditioners replaced large blocks of ice. Atomic and nuclear physicists think of energy in units of electron-volts, X-ray technicians think of energy in units of kilovolts (thousands of electron volts), electricity is commonly sold in units of kilowatt-hours, natural gas for heating is sold in units of therms, and on and on. Many of the more common conversion factors are on the inside front cover of the text.

B. Power

Power is the work done divided by the time taken to do it, and it is measured in foot-pounds per second or joules per second. A joule per second is called a watt. For example, if we do 50 foot-pounds of work in 5 seconds, the power is 50/5 = 10 foot-pounds per second. Similarly, 100 watts means that the agent is doing 100 joules of work per second. The horsepower is 550 foot-pounds per second.

C. Types of Energy

1.       Kinetic Energy

This is the energy associated with the motion of an object. If an object of mass m moves with speed v, then its kinetic energy is mv2/2. If m is measured in kilograms and v is in meters per second, then the energy is in joules. For example, a person with a mass of 80 kg walking at a speed of 2 m/s would have a kinetic energy of 80*22/2 = 160 joules. Be   careful with pounds – that is a unit of weight, not mass, and pounds cannot be used to compute kinetic energy directly. The easiest way of handling pounds is to convert the value to kilograms using the conversion factor in the front of the book: 1 kilogram is approximately 2.2 pounds or 1 pound is approximately 0.454 kilograms, so that as body whose weight is w pounds is equivalent to a mass of 0.454w kilograms. If you do this conversion, you must also convert the speed to meters per second if it is given in any other units.

If a gas is not too cold (so that it is not about to condense) then its internal energy is largely the kinetic energy of its atoms or molecules. The absolute temperature of a gas is proportional to the average of this kinetic energy. The macroscopic concepts of heating and cooling are equivalent to increasing or decreasing the average kinetic energy of the atoms or molecules that make up the gas. The temperature scale that realizes this proportionality is called the absolute or Kelvin scale, where the absolute temperature in Kelvin is related to the Celsius temperature by T= C + 273.15. Since absolute temperature is proportional to the internal kinetic energy of a gas, a gas would have no internal kinetic energy at all at a temperature of 0 Kelvin (a temperature of “absolute” zero). However, this is not the case – the relationship between temperature and internal kinetic energy breaks down at very low temperatures (or even at moderate temperature when a gas condenses into a liquid).

2.       Gravitational Potential Energy

This change in the gravitational potential energy is the work done when a mass is raised or lowered in a gravitational field. If the mass is raised, then some agent must push the mass “uphill” against the pull of gravity, and the potential energy of the mass has increased. The energy is called “potential” energy because it can be completely recovered (in principle) by letting the mass fall downhill again. If the mass falls freely, then the mass speeds up as it falls, and the potential energy at the top of the hill is converted to kinetic energy at the bottom. Alternatively, the mass might push against some other object as it falls and transfer its energy to that second object. If a mass of m kilograms is raised or lowered by h meters, then the change in gravitational potential energy is mgh, where g is the acceleration of gravity, which has a value of 9.8 m/s2 in the metric system. (Note the conversion of mass to weight by multiplying by the acceleration of gravity.) The change in potential energy is measured in joules in this case. A weight of p pounds raised or lowered by f feet has a change in potential energy of pf, which is measured in foot-pounds. Since the weight of the object is expressed in pounds, no conversion is needed.

3.       Electrical Potential Energy

This change in electrical potential energy is the work done when an electrical charge is moved in the vicinity of other charges. Since like charges repel, it takes work to push two like charges closer together, and that work, which must be done by some external agent, increases the electrical potential energy of the system. (You could think of pushing two like charges closer together as analogous to pushing a mass uphill.) This energy is also called “potential” energy because it can be recovered by letting the charges fly apart again. As with gravitational potential energy, when the charges are allowed to fly apart, the electrical potential energy is converted to kinetic energy or else the charges may interact with some other object and transfer energy to it. Electrical potential energy is also measured in joules, although the electron volt is also used when dealing with atoms or single protons and electrons. One electron-volt is 1.6´10-19 joules, which is an appreciable amount of energy when dealing with atomic particles. For example, the average kinetic energy of a molecule of air at room temperature is about 0.02 electron-volts.

4.       Chemical Energy

This is the energy released during a chemical reaction. The energy often appears as kinetic energy of the products, which we usually think of as “heat.” However, chemical reactions can also produce electrical potential energy, as in a battery, for example

5.       Mass Energy

It is possible to convert mass into energy and vice-versa. If a mass of m kilograms is converted to energy, the energy released is E= mc2, where c is the speed of light. If m is in kilograms and c is in meters per second then the energy is measured in joules. Since the square of the speed of light is a very large number, converting even a small amount of mass produces lots of energy. Conversely, it takes a lot of energy to produce even microscopic amounts of mass.

6. Electromagnetic energy

This energy is carried by electric and magnetic fields. Although these fields usually originate from charges and their motions, the fields themselves can transmit energy through empty space. For example, this is the principal way that energy from the sun reaches us. Depending on the frequency of the wave fields, we think of electromagnetic energy as light, radiant heat, x-rays or gamma rays, all of which are different manifestations of the same basic phenomenon.

D. Conservation of Energy

The principle of conservation of energy states that energy is neither created nor destroyed but only changes from one form to another. (In principle this should also include conversions between mass and energy) However, not all forms of energy are equally useful. Also, the conservation of energy does not say anything about the rate at which energy changes – only the overall change during the process is significant.