31. The volume of air and its weight per cubic foot change with the temperature. The following rule may be used to compute the change in volume, the pressure remaining constant:

Rule 4

Reduce both the original and the final temperatures to absolute temperatures. Multiply the original volume by the final absolute temperature and divide by the original absolute temperature. The quotient will be the final volume. Or, let

V

=

original volume;

V1

-

final volume;

T

=

original absolute temperature;

T1

-

final absolute temperature.

Then,

V

=

VT1

T

Example

What will be the volume of 400 cubic feet of air having a temperature of 150°, when it is cooled to 10°?

Solution

Applying rule 4,

V1

=

400 (460 +10)

=

308.19 cu. ft. Ans.

460+150

32. At constant pressure the weight of a given volume of air is inversely proportional to its absolute temperature. Let W denote the weight of a volume of air at the absolute temperature T, and W1, the weight of an equal volume at the absolute temperature T1 then,

w

•

w1

• •

T1

:

T,

or

w1

=

W T

and W

=

W1 T1

T1 '

T

Example

A chimney of 1 square foot area and 120 feet high is filled with hot air at a temperature of 450°; the temperature of the atmosphere is 60°; what is the difference between the weight of the air in the chimney, and the weight of a column of the outside air, of the same dimensions?

Solution

The volume of the air is 120 cubic feet. The weight of this volume of external air is (see Table 7) 120 X .07638 = 9.1656 pounds. The absolute temperature is 60 + 460 = 520°. Then,

W1

=

WT

=

9.1656X460 + 60

=

5.2375 lb.

T.

460 + 450

The difference in weight is, therefore, 9.1656 - 5.2375 = 3.9281 lb. Ans.