Explain: Gay-Lussac's Law.

(N/A) Pressure in well-inflated tyres of automobiles is almost constant,but on a hot summer day,a tyre may burst if the pressure is not adjusted properly. During winters on a cold morning,one may find the pressure in the tyres of a vehicle decreased considerably.
Law: At constant volume,the pressure of a fixed amount of a gas varies directly with the temperature.
Mathematically:
$p \propto T$ (at constant $V$) $\dots (Eq.-I)$
$p = K_{3} T$ (at constant $V$) $\dots (Eq.-II)$
So,$\frac{p}{T} = K_{3} =$ constant $\dots (Eq.-III)$
Law: "At constant volume,the ratio of pressure and absolute temperature of a gas is constant."
Formula for changes of temperature and pressure at constant volume: Suppose,at constant volume,initial pressure is $p_{1}$ and initial temperature is $T_{1}$,and final pressure is $p_{2}$ and final temperature is $T_{2}$.
According to Gay-Lussac's Law,$\frac{p_{1}}{T_{1}} = k_{3} = \frac{p_{2}}{T_{2}}$
Thus,$\frac{p_{1}}{T_{1}} = \frac{p_{2}}{T_{2}}$ $\dots (Eq.-IV)$
$\frac{p_{1}}{p_{2}} = \frac{T_{1}}{T_{2}}$ $\dots (Eq.-V)$
$p_{1} T_{2} = p_{2} T_{1}$ $\dots (Eq.-VI)$
Isochore Graph: The pressure $vs$ temperature (Kelvin) graph at constant molar volume is shown in the figure.