# 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.

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