Page 242 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 19] EXPANSION OF SOLIDS, LIQUIDS, AND GASES 227

When p 2 = 1 bar,
3
p 1 V 1 (16 bar)(3m ) 2
V 2 = = = 48 m
p 2 1 bar
SOLVED PROBLEM 19.9
What additional volume of air at 1 bar pressure must be pumped into the tank of Prob. 19.8 in order to
raise the gauge pressure to 25 bar?
When the absolute pressure of the air in the tank is

p 1 = 25 bar + 1 bar = 26 bar
the equivalent volume of air at p 2 = 1 bar is

3
p 1 V 1 (26 bar)(3m ) 3
V 2 = = = 78 m
p 2 1 bar
3
3
3
The additional volume of air is 78 m − 48 m = 30 m .

ABSOLUTE TEMPERATURE SCALES
When the temperature of a sample of gas is changed while the pressure on it is held constant, its volume changes
◦
◦
by 1/273 of its volume at 0 C for each temperature change of 1 C. If it were possible to cool a gas sample to
−273 C, its volume would diminish to zero. Since all gases condense into liquids at temperatures above −273 C,
◦
◦
◦
this experiment cannot be carried out; nevertheless, −273 C is a significant temperature.
◦
On the absolute temperature scale, the zero point is set at −273 C. Temperatures in this scale (also known
as the Kelvin scale) are expressed in kelvins (K); these units are equal to Celsius degrees. Thus
T K = T C + 273
The freezing point of water on the absolute scale is 273 K, and its boiling point is 373 K.
The Rankine scale is an absolute temperature scale based on the Fahrenheit scale. Absolute zero in the
Rankine scale is −460 F, and
◦
T R = T F + 460 ◦

◦
The freezing point of water in the Rankine scale is 460 R, and its boiling point is 672 R.
◦

CHARLES’S LAW
Because of the way the absolute temperature scales are defined, the relationship between the temperature and
volume of a gas sample at constant pressure can be expressed as

V 1 V 2
= p = constant
T 1 T 2
In this formula, which is called Charles’s law, V 1 is the volume of the sample at the absolute temperature T 1
and V 2 is its absolute temperature T 2 ; the formula only holds when the temperatures are expressed in an absolute
scale.