Question
Explain Charles’ law with the help of a diagram.
✓
Answer
Charles’ law $($Temperature$-$Volume relationship$):$
$i.$ Statement: At constant pressure, the volume of a fixed mass of a gas is directly proportional to its temperature in Kelvin.
$ii.$ Explanation:
For an increase of every degree of temperature, volume of the gas increases by $\frac{1}{273.15}. \ 15$ of its original value at $0 ^\circ C.$ This is expressed mathematically as follows:
$V _{ t }= V _0+\frac{t}{273.15} V_0$
Where $V_t$ and $V_0$ are the volumes of the given mass of gas at the temperatures t$ ^\circ C$ and $0 ^\circ C.$ Rearranging the Eq. $(1)$ gives
$V _{ t } = V _0\left(1+\frac{t}{273.15}\right)$
$\therefore V _{ t } = V _0\left(\frac{t+273.15}{273.15}\right)$
$V _{ t } = V _0\left(\frac{ T _{ t }}{ T _0}\right)$
where $T_t=t+273.15$ and $T_0=273.15$.
The equation $(3)$ on rearrangement takes the following form:
$\frac{ V _{ t }}{ T _{ t }}=\frac{ V _0}{ T _0}$
From this, a general equation can be written as follows:
$\frac{ V _1}{ T _1}=\frac{ V _2}{ T _2}$
$VT = K_2 =$ constant $($at constant $P$ and $n)$
$ \frac{ V }{ T }= K _2=$ constant $($at constant $P$ and $n)$
$ \therefore V = k _2$ to $R V \propto T \ldots \ldots . .(5)$
$iii.$ Schematic illustration of Charles’ law:
This shows that at constant pressure, gases expand on heating and contract on cooling.
$i.$ Statement: At constant pressure, the volume of a fixed mass of a gas is directly proportional to its temperature in Kelvin.
$ii.$ Explanation:
For an increase of every degree of temperature, volume of the gas increases by $\frac{1}{273.15}. \ 15$ of its original value at $0 ^\circ C.$ This is expressed mathematically as follows:
$V _{ t }= V _0+\frac{t}{273.15} V_0$
Where $V_t$ and $V_0$ are the volumes of the given mass of gas at the temperatures t$ ^\circ C$ and $0 ^\circ C.$ Rearranging the Eq. $(1)$ gives
$V _{ t } = V _0\left(1+\frac{t}{273.15}\right)$
$\therefore V _{ t } = V _0\left(\frac{t+273.15}{273.15}\right)$
$V _{ t } = V _0\left(\frac{ T _{ t }}{ T _0}\right)$
where $T_t=t+273.15$ and $T_0=273.15$.
The equation $(3)$ on rearrangement takes the following form:
$\frac{ V _{ t }}{ T _{ t }}=\frac{ V _0}{ T _0}$
From this, a general equation can be written as follows:
$\frac{ V _1}{ T _1}=\frac{ V _2}{ T _2}$
$VT = K_2 =$ constant $($at constant $P$ and $n)$
$ \frac{ V }{ T }= K _2=$ constant $($at constant $P$ and $n)$
$ \therefore V = k _2$ to $R V \propto T \ldots \ldots . .(5)$
$iii.$ Schematic illustration of Charles’ law:
This shows that at constant pressure, gases expand on heating and contract on cooling.
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