Let a and b be the quantities of heat employed successively in the first of the two operations, and let b' and a' be the quantities of heat employed successively in the second. As the final result of these two operations is the same, the quantities of heat employed in both should be equal. We have then
a + b = a' + b',
whence
a' - a = b - b'.
a' is the quantity of heat required to cause the gas to rise from 1° to 100° when it occupies the space abef.
a is the quantity of heat required to cause the gas to rise from 1° to 100° when it occupies the space abcd.
The density of the air is less in the first than in the second case, and according to the experiments of MM. Delaroche and Bérard, already cited on page 87, its capacity for heat should be a little greater.
The quantity a' being found to be greater than the quantity a, b should be greater than b'. Consequently, generalizing the proposition, we should say:
The quantity of heat due to the change of volume of a gas is greater as the temperature is higher.
