Charles’ Law
Christopher G. Hamaker, Illinois State University, Normal IL
© 2005, Prentice Hall
5 important properties of gases
1. Gases have an indefinite shape 2. Gases have low densities
3. Gases can compress 4. Gases can expand
5. Gases mix completely with other gases in the same
container
• One of the most amazing things about gases is that, despite wide differences in chemical properties, all the gases more or less obey the gas laws.
• The gas laws deal with how gases behave with respect to pressure, volume, temperature, and amount.
Boyle's Law: The Pressure-Volume Law
Charles' Law: The Temperature-Volume Law
Gay-Lussac's Law: The Pressure Temperature Law
Avogadro's Law: The Volume Amount Law
The Ideal Gas Law
Gas Law
Charles’ Law
• This is Charles’ Law.
V T at constant pressure.
V / T = k
• As the volume goes up, the temperature also goes up, and vice-versa.
• Also same as before, initial and final volumes and temperatures under constant pressure can be calculated.
V1 / T1 = V2 / T2 = V3 / T3 etc.
• Notice that Charles’ Law gives a straight line graph.
“The volume of a fixed mass of gas is directly proportional to its temperature (in kelvin) if the pressure on the gas is kept constant”
Jacques Charles (1746 - 1823)
∝
T is the temp. of the gas (in kelvins) k is a non-zero constant.
In these plots of volume versus temperature for equal-sized samples of H2 at three different pressures, the solid lines show the experimentally measured data down to −100°C, and the broken lines show the extrapolation of the data to V = 0.
The temperature scale is given in both degrees Celsius and kelvins. Although the slopes of the lines decrease with increasing pressure, all of the lines extrapolate to the same temperature at V = 0 (−273.15°C = 0 K).
The Relationship between Volume and Temperature
• In these plots of volume versus temperature for different amounts of selected gases at 1 atm pressure, all the plots extrapolate to a value of V = 0 at
−273.15°C, regardless of the identity or the amount of the gas.
The Relationship between Volume and Temperature
At constant pressure, the volume of a fixed amount of gas is directly proportional to its absolute temperature (in kelvins). This relationship, illustrated in Figure (right) is often referred to as Charles’s law and is stated mathematically as
0 at 273 at ( )
0 0
at ( C) at 0 C at 0 C
0
273 ( )
1 ( C)
273 1 1 ( C)
273
T K
T T K
T T T T
T
V
V T K
V V V T
V V T
=
° = ° = °
=
= + × × °
∴ = + °
0 at 273 at ( )
0 at 0 C at ( C)
0at 0 C 0at 0 C
at ( C)
0 at 0 C at ( ) 0at 0 C
0 0
at ( C) at 0 C at 0 C
0
273 ( )
{ ( C)+273}
273
( C)+ (273)
273 273
273 ( C)
1 ( C)
273
1 1 (
273
T K
T T K
T T T
T T
T T
T
T T K T
T T T T
T
V V T K
V
V T
V V
V T
V V V T
V V V T
V V T
=
= °
°
= ° = °
°
= °
= °
° = ° = °
=
= °
= °
= + °
= + × × °
∴ = + °C)
Charles’ Law
• The temperature where the pressure and volume of a gas theoretically reaches zero is absolute zero.
• If we extrapolate T vs. V graphs to zero volume, the
temperature is 0 K (Kelvin), or -273.15°C.
Charles’ Law
• Calculate the percentage error in verifying Charles’ Law using formular
• Estimate of absolute zero
2 1 1 2 0
1 2
t V t V
t V V
= −
−
1 2
1 2
1 1
Percent error 100%
V V
T T
V T
−
= ×
2 1 2 1
1 1
2 1 2 1
2 1
1 1
2 1
0
2 1
1 0 1
2 1
1 2 1 1 2 1 1
0 1
2 1 2 1
1 2 1 1 1 2 1 1 2 1 1 1 2 1 1 2
0 1
2 1 2 1 2 1
, ,
( )
0,
( )
( )
( )
V V V V
V at b a b V t
t t t t
V V
V V t t
t t
at V t t
V V
V t t
t t
V t t V t V t t t
V V V V
V t V t V t V t V t V t V t V t
t t
V V V V V V
− −
= + = = −
− −
− = − −
−
= =>
− = − −
−
− − − +
− = =
− −
− + − + + − −
= + = =
− − −
1 2
3
1 2
, : temperatures in Celsius , :volumes in cm
t t V V
