perature is due to the mechanical effect or work which must be spent in driving the particles of the air nearer together. Conversely, Heat is consumed in effecting mechanical work. Let a cylinder filled with compressed air be cooled to the temperature of the surrounding bodies; its elastic force is competent to produce mechanical work, (1) by moving a piston, or (2) in displacing the air in front of the cylinder.

If now this air is allowed to expand into the atmosphere, the air will be chilled, because mechanical work has been performed by the expenditure of the heat to which the elastic force of the air was due.

The relation which exists between heat and work is known as the mechanical equivalent of heat, or simply as Joule's equivalent. To determine for gases, suppose a tall cylindrical vessel

P

(Fig. 1.) C., whose section is equal to a square foot, and let PP be a piston without weight P Fig. 1. moving in the cylinder. If the

piston be placed so that the

height A P is one foot, it will inclose a cubic foot of air.

Now, if this air be heated 490° F., its volume will be doubled, and will raise the piston one foot, or to P' P'. In raising it has overcome the pressure of the atmosphere above the piston, or has lifted 15×144 = 2160 pounds one foot, and has performed work equal to 2160 foot pounds.

With the same amount of heat, only about one-fourth as much water would have been raised 490°, because the specific heat of air is 0.24 that of water.

•238

The weight of a cubic foot of air is .08 pound, °7.7) hence the heat imparted to perform the work of the air, would have heated only 0.08×0.24=.0192 pounds of water 490°.

This is equivalent to 9.4 pounds of water heated 1° Fah. Hence 9.4 thermal units have been required to raise 2160 pounds one foot high by the exhaustion of the air.

If the piston had been fixed so as to retain the air at a constant volume while being heated, the quantity of heat required to raise its temperature 490° would have been less than when expanding under a constant pressure in the ratio of 1.421 : 1.

Hence the thermal units required to raise the temperature of the cubic foot of air where kept. at a constant volume is found to be 9.4 1.421= 6.6 units. Deducting 6.6 units from 9.4 units, we find that the excess of heat imparted to the air when permitted to expand, is competent to raise 2.8 pounds of water 1° Fah.

This excess has been employed in performing the work of lifting 2, 160 pounds one foot high. Dividing 2, 160 by 2.8, we find that the quantity of heat required to raise one pound of water 1o Fah. is competent to lift 772 pounds a foot high. This is, therefore, the mechanical equivalent of one thermal unit.

In calculating the mechanical equivalent of heat, all the possible factors must be found and allowed for in order to obtain the exact equivalent. When a body falls freely through the air, a portion of its force will be expended by friction of the air, and the heat produced will be dissipated by radiation. If a body falling through a vacuum is suddenly arrested by collision with another, the heat generated will be in proportion to the height of the fall.

A portion of this heat may be again instantly converted into the mechanical motion of the rebound, and the remainder will be divided between the two bodies.

Now, since the height through which a body falls is proportioned to the square of the velocity attained (V = 8.02 √ H), the heat generated by the percussion of bodies moving in any direction will be as the squares of their velocities at the time of impact.

The dynamical theory also explains the evolution and consumption of heat which accompany changes in the volume or state of bodies.

Thus when heat enters a body, its actual energy is absorbed (1) in increasing the intensity of molecular motion, which is shown by a rise in the temperature, (2) in separating the molecules, as shown by expansion, and (3) in re-arranging its molecules, or causing a change of condition. The work performed is partly internal and partly

external. The exterior work is employed in overcoming external forces which resist the expansion, and the interior work is employed in separating and re-arranging the molecules within the mass of the body, by overcoming cohesion or affinity.

In whatever way we view it, the interior work performed by heat is enormous.

Thus, in expansion, a slight rise in temperature will produce a dilatation which would require the expenditure of tremendous mechanical power. Latent heat is merely a consumption of heat proportionate to the interior work required to overcome cohesion in melting or vaporizing a body.

The heat required to melt a pound of ice is one hundred and forty-three thermal units, which is equivalent to 110,396 foot-pounds.

The heat required to change boiling water into steam is 967 units, which is equivalent to 746,524 foot-pounds.

The actual energy of the heat may thus be measured by its equivalent of mechanical motion. Inasmuch as this motion may be again transformed into sensible heat by a contrary change of state, the atoms are said to possess a possible, or potential energy.

Thus, when a gas is liquefied by compression, external work is supplied, the interior work due to the cohesive force which draws the molecules together is transformed into sensible heat.

In like manner, the cohesive force which changes a liquid to a solid, performs interior work, and the potential energy becomes actual: that is, the latent heat becomes sensible. So also when two bodies unite by chemical affinity, the molecular motion is transformed to heat. Thus, when of a pound of hydrogen combines with of a pound of oxygen, one pound of steam is produced, and 6,892 thermal units are evolved, which are equivalent to 5,320,624 foot-pounds.

The molecular force evolved in changing a mixture of these gases to a pound of ice will therefore be:

This is equivalent to the force required to raise one ton to a height of 3,098 feet, or 3,098 tons one foot high.

Molecular forces are, therefore, by far the most powerful of any with which we are acquainted.