ENERGY

Now that we have become familiar with what is meant by work, let us consider a related but more general physical quantity, namely, energy.  If anything has the capacity to perform work, it is said to possess energy.  The amount of its energy is measurable in terms of the amount of work it can perform.  Hence, energy is measurable in units of work—ergs, joules, or foot-pounds.

Potential Energy.  A stretched spring does work when it contracts.  A weight upon a table does work in being lowered to the floor.  Work is done when a piece of iron is drawn to a magnet.  Hence, each of those systems possesses energy which is manifested by the amount of work that it can do in changing from one position or configuration to another.  Energy of this kind obviously is associated with the position or configuration of a material system and is known as potential energy.

Chemical systems, such as gunpowder, gasoline, coal, dry cells, storage batteries and the like, have the capacity of performing work when they undergo chemical changes.  This too is potential energy and is dependent upon the internal configuration of the atoms with respect to each other.

Kinetic Energy.  Imagine a flywheel mounted upon a horizontal axle with as nearly as possible frictionless bearings, and a cord with a suspended weight attached so as to wind around the axle.  First, wind the system up and then release it.  As the weight falls, the flywheel will continuously increase its angular velocity.  When the weight reaches its lowest position, the cord will begin to wind around the axle in the opposite direction, and the weight will be raised.  At the same time, the flywheel will be slowed down, coming finally to rest when the weight has regained its original elevation.  Then, if not arrested, the process will repeat itself in the opposite direction.

In the initial and the final stages of this experiment the system possesses potential energy—that of the raised weight.  In the middle stage, when the weight has reached its lowest position, its potential energy is a minimum.  Still, however, the system has a capacity to do work as demonstrated by its lifting the weight back to its original elevation.  This energy obviously resides in the motion of the flywheel.  In fact, if we set a flywheel in motion by any method and then bring it to rest by having it lift a weight, we find that the number of joules of work it can do is proportional to the square of its angular velocity (number of revolutions per unit time).

In the same manner we can bring an automobile coasting on a level road to rest by making it lift a weight.  The work it can do is found to be proportional to its mass and the square of its speed.  In fact, the work it could do in this manner is:

Work=mass x speed2

Bodies, therefore, possess energy in virtue of their state of motion.  Work must be performed upon them to set them moving and must be done by them in coming to rest again.  This energy, due to motion, is called kinetic energy.

Heat.  When work is performed on a system, it may not increase either the potential or the kinetic energy of the system.  It may be completely dissipated by friction.  An automobile or a flywheel can be brought to rest by means of brakes.  A weight can be lowered at constant speed if properly braked.  In all such cases heat is produced where the friction occurs.  On a long grade the brakes of an automobile may become so hot as to burn out.  Drills become heated when boring.  Tools are heated by grinding.

The conclusion is that when a body loses kinetic or potential energy due to friction heat is always produced.  Hence, heat must be a form of energy.  Does a given amount of work always produce the same amount of heat? To answer this question we must devise a way to measure heat.

Measurement of Heat.  To measure heat, we must first distinguish between the temperature of a body and the quantity of heat it contains.  Our primitive recognition of temperature is by means of our sense of feel.  The quantity of heat a body contains is related both to its temperature and to the size of the body.  Thus, a gallon of water contains four times as much heat as a quart of water at the same temperature.  How the quantity of heat is related to the temperature can only be determined after we have found how to measure temperature.

Measurement of Temperature.  Our sense of feel is not very reliable for determining temperatures, so we must devise a temperature measuring instrument.  This we do by noting that gases, liquids, and solids all change volume as their temperature is changed.  Usually, but not in all cases, the volume increases with increase of temperature.  In addition to this we have certain invariant points of fixed temperature like that of melting ice, and boiling water at constant pressure.  By means of the expansion of a given material between these fixed temperatures we can measure intermediate temperatures.

We may define the temperatures of melting ice and of boiling water at a pressure of one standard atmosphere (one standard atmosphere is defined to be the pressure exerted by a column of mercury 76.0 centimeters high due to the attraction of standard gravity, or 1.01325×106 dynes per square centimeter) to be anything we like, but the choice of these temperatures determines the thermometric scale.

If we let 0° be the temperature of melting ice and 100° that of boiling water, we have the Centigrade scale.  If we let 32° be the temperature of melting ice and 212° that of boiling water, we have the Fahrenheit scale.

For the intermediate temperatures, our best thermometric substance is hydrogen gas.  If we let V0 be the volume of a given quantity of hydrogen gas at the temperature of melting ice and at a pressure of 1 atmosphere, and V100 that of the same gas at the temperature of boiling water and a pressure of 1 atmosphere, then by dividing the difference between these two values into 100 equal parts we have a volume scale for the gas to which we relate the corresponding temperatures.  For example, at some unknown temperature the gas has a measured volume V.  The temperature in ° C.  then is:

t= V −V 0

V 100−V 0

100

If V should be one-fourth the difference between V0 and V100, the temperature would be 25° C.; if one-half, the temperature would be 50° C., etc.

The same procedure is used for the Fahrenheit scale except in this case the interval between freezing and boiling is taken to be 180° instead of 100°, and freezing is defined to be 32°.

The familiar mercury thermometers are handier to use.  They are calibrated, however, by temperatures originally established by a hydrogen thermometer.

Absolute Scale of Temperature.  There is one more scale of great scientific importance that should be mentioned now because we shall need to make use of it in our next lesson.  This is the absolute scale.

It is found by experiment that for each degree Centigrade between 0° C.  And 100° C., the volume of hydrogen gas increases by a constant amount of 1/273.2 of its volume at 0° C., V0.  At this same rate of volume change, the volume would decrease to zero at a temperature of -273.2° C., which suggests that this may be the lowest possible temperature obtainable.  Elaborate experimentation has demonstrated that this is the case, and temperatures within a fraction of a degree of this amount have been obtained.

It seems reasonable, therefore, to call the lowest possible temperature, the absolute zero of temperature.  If we call this 0° absolute, and otherwise use the Centigrade scale, then the melting point of ice becomes 273.2° absolute and the boiling point of water 373.2° absolute.

Conversion factors between the thermometric scales are as follows:

1.8° F.  = 1.0° C.

1.0° F.  =  ° C.  χ° F.  =  T° C.+32 χ° C.  =  (T° C.-32)

χ° abs.  = T° C.+273.2

Quantity of Heat.  To measure the amount of heat, we require a unit of measurement, whose choice, like that of all other units of measurement, is arbitrary.  In the Metric system we take this to be the amount of heat required to raise the temperature of 1 gram of water 1° C.  We call this the gram calorie.  A kilogram calorie is 1,000 gram calories, or the heat required to raise the temperature of a kilogram of water 1° C.

In the English system the corresponding unit is the British thermal unit, or therm, defined as the amount of heat required to raise the temperature of 1 pound of water 1° F.

Since the heat required per degree varies slightly with temperature, for very exact measurements we must also specify the temperature at which the measurement is to be made.  The most common procedure is to take the mean, or average, values over the range from 0° C.  To 100° C.  These will be understood to be the values employed here.

By converting ° F.  to ° C.  and pounds to grams we can easily determine the conversion factors between the English and Metric units:

1 kilogram calorie = 3.9685 British thermal units

1 British thermal unit = 251.98 gram calories

= 0.25198 kilogram-calories

Work and Heat.  We are now in a position to answer the question propounded earlier: How much heat is produced by friction from a given amount of work? To determine this all we need is a heat insulated vessel filled with water, into which a shaft from the outside extends and terminates in some kind of a brake mechanism.  On the external end of the shaft is a pulley around which a cord supporting a weight is wound.  The weight falls slowly, and heat is generated by the brake inside the vessel.  By noting the temperature rise and the quantity of water heated, the number of calories of heat can be computed; by knowing the weight and the distance it descends the amount of work can be computed.  Then we know the quantity of heat generated by a known amount of work.

The first experiment of this kind was performed by Joule in England about 1845.  Subsequently, numerous such experiments have been performed with great precision.  As a result, it has been found that a given amount of work always produces the same amount of heat: 4.186 joules of work produce 1 gram calorie of heat; 777.97 foot-pounds of work produce 1 BTU of heat.

Thus, since 4.186 joules are equal approximately to 3.1 foot-pounds, it is clear that a 1-pound weight falling 3.1 feet will produce 1 gram-calorie of heat; if a 1-pound weight falls 778 feet and its energy is converted into heat, the amount of heat will be 1 British thermal unit.  Hence, the heat generated by a waterfall 778 feet high would be sufficient to raise the temperature of the water at the foot of the fall 1 degree Fahrenheit.  Actually, unless the quantity of water is large, a considerable fraction of this heat will be lost to the surrounding air and by evaporation of the falling water, but the heat generated, counting the above losses, is still 1 British thermal unit per pound of water.

Since friction is never completely eliminated, we see that in all processes involving work, energy in the form of work is continuously dissipated and an equivalent amount of energy in the form of heat is produced.

References:

  • This Mechanical World, Mott-Smith.
  • Heat and Its Workings, Mott-Smith.
  • The Story of Energy, Mott-Smith.
  • A Textbook of Physics, (Vol.  I, Mechanics; Vol.  II, Heat and Sound), Grimsehl