Relation between Pressure, Density, and Temperature of a Gas

 Relation between Pressure, Density, and Temperature of a Gas

AIR AT REST, THE ATMOSPHERE AND STATIC LIFT 13

ii. Relation between Pressure, Density, and Temperature of a Gas

By the experimental laws of Boyle and Charles, for constant

temperature the pressure of a gas is proportional to its density ; for

constant volume the pressure of a gas is proportional to its absolute

temperature. The absolute temperature is denoted by T and, if 6 is

the temperature on the centigrade scale, is given by

T = + 273.

Combining these laws, we have, for a given mass of a particular

gas:

pV^Bt (8)

where V is the volume, or, if V is the volume of 1 lb.,

P/9=gBi: (9)

B is a constant which is made characteristic of a particular gas by

treating 1 lb. of the gas ; it is then evaluated from measurements of

pressure and volume at a known temperature. It follows that B

will vary from one gas to another in inverse proportion to the

density under standard conditions of pressure and temperature.

If N is the ixumber of molecules in V, N will, by Avogadro's law,

be the same for all gases at constant p and T. Hence, writing pV/N

= B'T, B' is an absolute constant having the same value for all

gases. Equation (9) is more convenient, however, and the variation

of B is at once determined from a table of molecular weights.

Some useful data are given in Table II. It will be noticed that, if p

is kept constant, B measures the work done by the volume of gas in

expanding in consequence of being heated through unit temperature

change. The units of B are thus ft.-lb. per lb, per degree centigrade,

or ft. per C.