But if the cubic foot of steam were allowed to expand so as to occupy more space, then additional heat is necessary to prevent its condensation.
The relation between the temperature, pressure, and weight of steam is not quite proportional to the volume, because steam is not a perfect gas, and does not, therefore, strictly follow Mariotte’s law.
A perfect gas is one that during expansion or compression follows the law laid down by Boyle and Mariotte, this law being that, if maintained at a constant temperature, the volume is inversely proportional to the pressure.
For example, the quantity of gas that, if confined in a cubic inch of space, would give a pressure of 80 lbs. per square inch, would give a pressure twice as great (or 160 lbs. per inch of area), if confined in one-half the space, that is, if compressed into one-half of a cubic inch. Conversely, if the cubic inch was allowed to expand until its pressure was 40 lbs., it would occupy 2 cubic inches of space, assuming, of course, that the temperature remains the same. Since, however, if a gas be compressed, its temperature is increased by reason of the friction of the particles moving one upon the other, the law of Mariotte may be better explained as follows:
Suppose we have three vessels, A, B, and C, filled with a fluid which is a perfect gas, the temperatures being equal. Let the pressure be: A 40, B 80, and C 160 lbs. per square inch, then 2 cubic inches of the fluid in B will weigh the same as 4 cubic inches in A, because that in B is at twice the pressure of that in A, and the 2 cubic inches in B will weigh the same as 1 cubic inch in C, because its pressure is one-half that of C, or, what is the same thing, whatever number of cubic inches of the fluid in C it takes to weigh a pound, it will take twice as many in B, and four times as many in A to weigh one pound.
But steam is not a perfect gas, as is evidenced by the fact that its volume does not increase in a ratio inverse to its pressure. For example, if a cubic inch of water be evaporated into steam at a pressure of 14.7 lbs. per square inch, its volume will be 1644 cubic inches, and its temperature 212° Fahrenheit.
But if the cubic inch of water be evaporated into steam at twice the pressure, which is 29.4 lbs per square inch, its volume will be 838 inches.
The volume then is not inversely as the pressure, although the actual quantity and weight remain the same, as is proven by the fact that if the steam at either pressure were condensed it would pass back into the cubic inch of water from which it was generated.
This may be accounted for in the difference in the boiling point of the water in the two pressures, or in other words, by the difference in the temperatures; thus the boiling point of the water at a pressure of 14.7 lbs. is 212°, while that for the pressure of 29.4 is increased about 38.4 degrees, and the steam is at the higher pressure expanded by these 38.4 degrees of heat, which adds to its pressure, although not affecting its actual quantity or weight.
The amount of this expansion may be estimated as follows: