# JEE Main & Advanced Chemistry States of Matter Charles Law

## Charles Law

Category : JEE Main & Advanced

(1) French chemist, Jacques Charles first studied variation of volume with temperature, in 1787.

(2) It states that, “The volume of a given mass of a gas is directly proportional to the absolute temperature $(={{\,}^{o}}C+273)$ at constant pressure”.

Thus, $V\propto T$ at constant pressure and mass

or $V=KT=K(t({{\,}^{o}}C)+273.15)$ ,   (where k is constant),

$K=\frac{V}{T}$ or $\frac{{{V}_{1}}}{{{T}_{1}}}=\frac{{{V}_{2}}}{{{T}_{2}}}=K$ (For two or more gases)

(3) If $t={{0}^{o}}C$, then $V={{V}_{0}}$

hence,    ${{V}_{0}}=K\times 273.15$

\ $K=\frac{{{V}_{0}}}{273.15}$

$V=\frac{{{V}_{0}}}{273.15}[t+273.15]={{V}_{0}}\left[ 1+\frac{t}{273.15} \right]={{V}_{0}}[1+{{\alpha }_{v}}t]$

where ${{\alpha }_{v}}$ is the volume coefficient,

${{\alpha }_{v}}=\frac{V-{{V}_{0}}}{t{{V}_{0}}}=\frac{1}{273.15}=3.661\times {{10}^{-3}}{{\,}^{o}}{{C}^{-1}}$

Thus, for every ${{1}^{o}}$ change in temperature, the volume of a gas changes by $\frac{1}{273.15}\left( \approx \frac{1}{273} \right)$ of the volume at ${{0}^{o}}C$.

(4) Graphical representation of Charle's law : Graph between V and T at constant pressure is called isobar or isoplestics and is always a straight line. A plot of V versus $t({{\,}^{o}}C)$ at constant pressure is a straight line cutting the temperature axis at $-{{273.15}^{o}}C$. It is the lowest possible temperature.

(5) At constant mass and pressure density of a gas is inversely proportional to it absolute temperature.

Thus, $d\propto \frac{1}{T}\propto \frac{1}{V}$           $\left[ \because V=\frac{\text{mass}}{\text{d}} \right]$

or        $\frac{{{d}_{1}}}{{{d}_{2}}}=\frac{{{T}_{2}}}{{{T}_{1}}}=\frac{{{V}_{2}}}{{{V}_{1}}}=......=K$

(6) Use of hot air balloons in sports and meteorological observations is an application of Charle's law.

LIMITED OFFER HURRY UP! OFFER AVAILABLE ON ALL MATERIAL TILL TODAY ONLY!

You need to login to perform this action.
You will be redirected in 3 sec