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Q.
The volume of a given mass of a gas at $27^{\circ} C ,\, 1\, atm$ is $100\, cc .$ What will be its volume at $327^{\circ} C$ ?
Kinetic Theory
Solution:
We have to convert the given temperatures in kelvin. If pressure of a given mass of the gas is kept constant, then $V \propto T$
$\Rightarrow \frac{V}{T}=$ constant $\left[V=\text { Volume of gas} \\ T=\text { Temperature of gas }\right]$
$\Rightarrow \frac{V_{1}}{T_{1}}=\frac{V_{2}}{T_{2}}$
$\Rightarrow V_{2}=V_{1}\left(\frac{T_{2}}{T_{1}}\right)$
Here we must convert the given temperature in kelvin.
$T_{1}=273+27=300\, K$
$T_{2}=273+327=600\, K$
But $V_{1}=100\, cc$
$V_{2}=V_{1}\left(\frac{600}{300}\right)$
$\Rightarrow V_{2}=2 V_{1}$
$\therefore V_{2}=2 \times 100=200\, cc$