Charle's law states that at a constant pressure, the volume of a gas increases or decreases by 1/273 of its original volume for each 1 degree Celsius increase or decrease in temperature. Specifically, the volume is directly proportional to the absolute temperature. This relationship has been verified experimentally by plotting graphs of volume versus temperature, which produce straight lines passing through the origin, indicating a direct proportionality. The law allows for calculations of gas volume changes with temperature changes and has applications like filling hot air balloons due to air's decreasing density when heated.

1. Charle’s law

2. Charle’s Law:
Jacques Charles, a French chemist studied the variation of volume of
given mass of gas with temperature at constant pressure. The result of
his study are stated in the form of law which is known as Charle’s Law.
It states that, “At a constant pressure, the volume of a given mass of a
gas increases or decreases by 1/273 of its volume at 0°C for each
degree Celsius rise or fall in temperature.’’
Let Vo be the volume of a given mass of a gas at 0°C. Then, according to
Charle’s Law

4. Similarly, if the gas be cooled,
Volume of the gas at -1oc =(1-
1
273
)Vo
Volume of the gas at -5oc =(1-
5
273
)Vo
Volume of the gas at -toc =(1-
t
273
)Vo
Volume of the gas at -273oc =(1-
273
273
)Vo
= 0

5. Thus, at -273oc, the volume of the gas becomes theoretically equal to
zero. In fact all gases become liquid or solid before this temperature is
reached. This lowest hypothetical temperature, -273oc is called
absolute zero. This is the lowest temperature that is theoretically
possible. At this temperature, molecules have no kinetic energy, no
velocity and occupy no volume theoretically

6. Again, if V1 be the volume of gas at t1 and
V2 be the volume of gas at t2 then

7. Where T = t + 273 and T is the absolute scale or kelvin scale of
temperature. i.e. T1 and T2 are corresponding absolute temperature.

8. From the above expression,

9. Hence, Charle’s law can also be stated as “The volume of a given mass
of gas is directly proportional to the absolute scale of temperature at
constant pressure.”

10. Thus a plot of V vs T at constant pressure will be a
straight line passing through the origin.

11. Kelvin scale of temperature:
A British scientist Lord Kelvin suggested a new scale of temperature
known as absolute or kelvin scale of temperature. The zero point on
this scale correspond to -273oc. The temperature on kelvin scale are
indicated simply by writing the letter K.
Temperature on Celsius scale can be converted into temperature on
kelvin scale by adding 273. That is
Temperature on kelvin scale = 273 + temperature on Celsius scale.
T(K)= 273+ t(oc)

12. Experimentally verification of Charle’s law
Charle’s law is verified experimentally by plotting a graph between
volume and temperature at constant pressure which gives a straight
line. This line extrapolation intersects the temperature axis at -273oC.

13. Fig: plot of V against temperature oc

14. From the above graph it is clear that the volume of the gas become 0 at
-273oC theoretically. This is the lowest possible temperature at which
the gas occupies zero volume and has no kinetic energy. This
temperature has never been realized in any laboratory of the world so
far.

15. Significance (application) of Charle’s law:
Air expands on heating and hence its density decreases. Thus hot air is
lighter than the atmospheric air. This fact is made use of in filling hot air
in the balloons which rise up for meteorological observations.

16. Numericals
1. 20 ml of hydrogen measured at 15oc are heated to 35oc. What is the
new volume at the same pressure? Ans:21.38 ml
2. At what temperature centigrade will be the volume of a gas at 0oc
double itself, pressure remaining constant? Ans: 273oc
3. What volume of air will be expelled from a vessel containing 400
cm3 at 7oc when it is heated to 27oc at the same pressure?
Ans:28.6cm3
4. It is desired to increase of the volume of a gas by 20% without
changing the pressure. To what temperature the gas must be
heated if the initial temperature of the gas is 27oc? Ans: 87oc