The expansion of air for every increase of 1° Cent. is ·003665 (1 ∕ 273), for every increase of 1° Fahr. is ·00203 (1 ∕ 492). Thus if the air in a room is 20° F. warmer than that outside, it will be expanded to 1 ∕ 25 additional bulk.
Thus if M = volume of a given air at 32°, with the barometer at 30 inches, and
M1 = volume at temperature t° above 32°, while a = co-efficient of expansion for each degree of elevation of temperature, then the dilatation effected by heat will be expressed by the formula—
M1 = M (1 + at).
When the temperature is decreasing
M1 = M (1-at).
If the air in a chimney flue is cooler than the air of the room with which it communicates, it will flow down into the room. It is the object of an economical fire-place to cause the chimney to act as an outlet for the products of combustion and for the impurities of the air of the room with the smallest possible waste of heat. Short of producing a down draught of cold air and smoke, the smaller the difference between the temperature of the air of a room and of the air escaping near the top of the chimney, the greater the economy of fuel.
The movement of air in flues and other outlets is governed by general laws, like those governing the general movements of fluids, but allowances require to be made for friction in the channels of entrance and outlet.
The theoretical velocity, when friction is not taken into account, may be calculated by a formula based on what is known as the law of Montgolfier, or the law of spouting fluids. According to this law, fluids pass through an opening in a partition with the same velocity as a body would attain in falling through a height equal to the difference in depth of the fluid on the two sides of the partition, i.e. to the difference of pressure on the two sides. Thus, if AB equals the height of a column of air at, say, 50° F., and AC is the height of the same quantity of air heated to 60°, then the velocity with which the warmer air ascends will be that which a body would acquire in falling from C to B.