Study of Gas Laws — Question 9

V₁ = Initial volume of the gas = V cc
T₁ = Initial temperature of the gas = 240 K
T₂ = Final temperature of the gas = 127°C = 127 + 273 = 400 K
V₂ = Final volume of the gas = ?

By Charles' Law:

$\dfrac{\text{V}_1}{\text{T}_1} = \dfrac{\text{V}_2}{\text{T}_2}$

Substituting the values :

$\dfrac{\text{V}}{240} = \dfrac{\text{V}_2}{400} \\[1em] \text{V}_2 = \dfrac{400 \times \text{V}}{240} \\[1em] \text{V}_2 = \dfrac{5\times \text{V}}{3}$

Increase in vol. = $\dfrac{5\text{V}}{3}$ - V = $\dfrac{2\text{V}}{3}$

Percentage increase in vol. = $\dfrac{\text{Increase}}{\text{Original}}$ x 100 = $\dfrac{2\text{V}}{3\text{V}}$ x 100 = 66.67%

∴ Percentage increase in the volume of the gas = 66.67%