Refrigeration & Air Conditioning Technology, 8e - 33

33

Unit 2 Matter and Energy

CHARLES' LAW
In the 1800s, a French scientist named Jacques Charles made
discoveries regarding the effect of temperature on gases.
Charles' law states that at a constant pressure, the volume of
a gas varies directly as to the absolute temperature, and at a
constant volume, the pressure of a gas varies directly with the
absolute temperature. Stated in a different form: When a gas
is heated and if it is free to expand, it will do so, and the volume will vary directly as to the absolute temperature; if a gas
is confined in a container that will not expand and it is heated,
the pressure will vary directly with the absolute temperature.
This law can also be stated with formulas. Two formulas
are needed because one part of the law pertains to pressure and
temperature and the other part to volume and temperature.
This formula pertains to volume and temperature:
V1
T1

5

V2
T2

where V1 5 original volume
V2 5 new volume
T1 5 original temperature
T2 5 new temperature

V1 5 2000 ft3
T1 5 75°F 1 460°R 5 535°R (absolute)
V2 5 unknown
T2 5 130°F 1 460°R 5 590° R (absolute)
We must mathematically rearrange the formula so that the
unknown is alone on one side of the equation.

V2 5

V1 3 T2

T1

5

P2
T2

where P1 5 original pressure
T1 5 original temperature
P2 5 new pressure
T2 5 new temperature
If a large natural gas tank holding 500,000 ft3 of gas is stored
at 70°F in the spring and the temperature rises to 95°F in the
summer, what would the pressure be if the original pressure
was 25 psig in the spring?
P1 5 25 psig 1 14.696 (atmospheric pressure)
or 39.696 psia
T1 5 70°F 1 460°R or 530°R (absolute)
P2 5 unknown
T2 5 95°F 1 460°R or 555°R (absolute)

P2 5
P2 5

P1 3 T2
T1
39.696 psia 3 5558R
5308R

P2 5 41.57 psia 2 14.696 5 26.87 psig

GENERAL LAW OF PERFECT GAS
A general gas law, often called the general law of perfect gas,
is a combination of Boyle's and Charles' laws. This combination law is more practical because it includes temperature,
pressure, and volume.
The formula for this law can be stated as follows:

T1
2000 ft3 3 5908R
5358R

V2 5 2205.6 ft3
This result shows that the air expanded when heated.

P1 3 V1
T1

5

P2 3 V2
T2

where P1 5 original pressure
V1 5 original volume
T1 5 original temperature
P2 5 new pressure
V2 5 new volume
T2 5 new temperature

Figure 2.7 Air expands when heated.

2000 FT3 OF
758F AIR

P1

Again, the formula must be rearranged so that the unknown
is on one side of the equation by itself.

If 2000  ft3 of air is passed through a gas-fired furnace and
heated from 75°F room temperature to 130°F, what is the
volume of the air leaving the heating unit? See Figure 2.7.

V2 5

The following formula pertains to pressure and
temperature:

BLOWER

HEAT

BECOMES

2205.6 FT3 OF
1308F AIR

For example, 20 ft3 of gas is being stored in a container at
100°F and a pressure of 50 psig. This container is connected
by pipe to one that will hold 30  ft3, for a total volume of
50  ft3, and the gas is allowed to equalize between the two



Refrigeration & Air Conditioning Technology, 8e

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