A given amount of gas A is confined in a chamber of constant volume. When the chamber is immersed in a bath of melting ice, the pressure of the gas is 100 cm Hg.

(a) What is the temperature, when the pressure is 10 cm Hg?

(b) What will be the pressure, when the chamber is brought to 100°C?

(a) P₁ = Initial pressure of the gas = 100 cm Hg

T₁ = Initial temperature of the gas = 273 K

P₂ = Final pressure of the gas = 10 cm Hg

T₂ = Final temperature of the gas = ?

V₁ = V₂ = V [constant volume]

By Gas Law:

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

Substituting the values :

$\dfrac{100 \times \text{V}}{273} = \dfrac{10 \times \text{V}}{\text{T}$2} \\[1em] \text{T}2 = \dfrac{ 273}{10} \\[1em] \text{T}_2 = 27.3 \text {K} \\[1em]

∴ When the pressure is 10 cm Hg, the temperature is 27.3 K.

(b) P₁ = Initial pressure of the gas = 100 cm Hg

T₁ = Initial temperature of the gas (ice point) = 273 K

P₂ = Final pressure of the gas = ?

T₂ = Final temperature of the gas = 100°C = 273 + 100 = 373 K

V₁ = V₂ = V [constant volume]

By Gas Law:

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

Substituting the values :

$\dfrac{100 \times \text{V}}{273} = \dfrac{\text{P}$2 \times \text{V}}{373} \\[1em] \text{P}2 = \dfrac{ 37300}{273} \\[1em] \text{P}_2 = 136.63 \text { cm of Hg} \\[1em]

∴ When the chamber is brought to 100°C, the pressure is 136.63 cm Hg.