Derive mathematical expression for Charles law Give its Significance.

Explanation

Mathematical expression of Charles.s law
Let `V_0` be the volume of a fixed mass of a gas at `0^@C`. Let V be its volume at temperature `""^@C` at constant pressure . Then , according to Charles.s law,
`V=V_0+V_0/273 t` (when P is constant)
`V=(1+t/273)=V_0((273+t)/273)`....(i)
`V=V_0/273 T` where T=273 + t
For a given mass of a gas,
`V_0/273`= constant
`therefore` V = k x T (where k is constant)
`V prop T` and `V/T=k`
Suppose , a gas occupies `V_1 "cm"^3` at `T_1` temperature and `V_2 "cm"^3` at `T_2` temperature , then by Charles.s law
`V_1 prop T_1`
`V_1= kT_1` (k is constant )
`V_1/T_1=k` and `V_2 prop T_2` or `V_2/T_2`= k
`therefore V_1/T_1=V_2/T_2=k` (at constant pressure)
Significance of Charles.s law
Volume of a given mass of a gas is directly proportional to its temperature , hence density decreases with an increase in temperature.