To what temperature must a gas at 300 K be cooled down in order to reduce its volume to $\dfrac{1}{3}$rd of its original volume, pressure remaining constant?

V₁ = Initial volume of the gas = V

T₁ = Initial temperature of the gas = 300 K

V₂ = Final volume of the gas = $\dfrac{1}{3}$V

T₂ = Final temperature of the gas = ?

By Charles' Law:

$\dfrac{\text{V}$1}{\text{T}1} = \dfrac{\text{V}2}{\text{T}2}

Substituting the values :

$\dfrac{\text{V}}{300} = \dfrac{\dfrac{1}{3}\text{V}}{\text{T}$2} \\[1em] \text{T}2 = \dfrac{300}{3} \\[1em] \text{T}_2 = 100 \text{ K}

∴ Final temperature = 100 K