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KINETIC THEORY OF GASES | Up
Aerographers Mate, Module 05-Basic Meteorology | Next
EQUATION OF STATE |
Boyle’s law does not consider changes in
temperature. Since our atmosphere is constantly
changing temperature at one point or another,
temperature must be considered in any practical
application and understanding of gas laws.
CHARLES’ LAW
In the section on the kinetic theory of gases, it was
explained that the temperature of a gas is a measure of
the average speed of the molecules of the gas. It was
also shown that the pressure the gas exerts is a measure
of the number of times per second that the molecules
strike the walls of the container and the speed at which
they strike it. Therefore, if the temperature of a gas in a
closed container is raised, the speed of the molecules
within the gas increases. This causes the molecules to
strike the sides of the container more often per second
and with more force because they are moving faster.
Thus, by increasing the temperature, the pressure is
increased.
Charles’ law states if the volume of an enclosed gas
remains constant, the pressure is directly proportional
to the absolute temperature. Therefore, if the absolute
temperature is doubled, the pressure is doubled; if the
absolute temperature is halved, the pressure is halved.
Experiments show that the volume increases by 1/273
for a 1°C rise in temperature. (Remember, 0°C is equal
to 273°K.) An example of Charles’ law is a bottle of
soda or beer. When the soda or beer is cold, very little
pressure is released when the bottle is opened. When a
warm soda or beer is opened, it often results in enough
pressure buildup in the bottle to squirt soda or beer out
of the top. Sometimes, warm soda or beer explodes
spontaneously when exposed to too much direct heat
such as sunlight.
The formulas for Charles’ law are as follows:
VT’ = V’T, where pressure is assumed to be
constant, and
PT’ = P’T, where volume is constant
V = initial volume
T = initial temperature (absolute)
V’ = new volume
T’ = new temperature (absolute)
For example, assume that 10 cm3 of a gas has a
temperature of 200° absolute. If the temperature is
increased to 300° absolute, what will be the new
volume? Applying the formula, we have
V = 10 cm3
T = 200°K
V’ = Unknown in cm3
T’ = 300°K
10 · 300 = V’ · 200
3000 = V’ · 200
V’ =3000
200
V’ = 15 cm3
The same type relationship can be computed by
applying T’ (new temperature) and P’ (new pressure)
using the formula PT’ = P’T where the volume is
assumed to remain constant.
UNIVERSAL GAS LAW
The universal gas law is a combination of Boyle’s
law and Charles’ law. It states that the product of the
initial pressure, initial volume, and new temperature
(absolute scale) of an enclosed gas is equal to the
product of the new pressure, new volume, and initial
temperature. The formula is as follows:
PVT’ = P’V’T
P = initial pressure
V = initial volume
T = initial temperature (absolute)
P’ = new pressure
V = new volume (absolute)
T = new temperature (absolute)
For example, assume the pressure of a 500 cm3
volume of gas is 600 mb and the temperature is 30°C
(303 absolute). If the temperature is increased to 45°C
(318° absolute) and the volume is decreased to 250
cm3, what will be the new pressure of the volume?
Applying the formula, we have
P = 600 mb
V = 500 cm3
T = 303°K
P’ = Unknown pressure in mb
V’ = 250 cm3
T’ = 318°K
600 · 500 · 318 = P’ · 250 · 303
95,400,000 = P’75,750
P’ =95400000
75
750
,
,
,
P’ = 1,259.4 mb
2-9
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