A certain mass of a gas occupies 2 Litres at 27°C and 100 pascal. Find the temperature when volume and pressure become half of their initial values.

Initial conditions [S.T.P.] :

P₁ = Initial pressure of the gas = 100 Pascal

V₁ = Initial volume of the gas = 2 Litres

T₁ = Initial temperature of the gas = 27°C = 27 + 273 = 300 K

Final conditions :

P₂ (Final pressure) = 50 Pascal
V₂ (Final volume) = 1 litre
T₂ (Final temperature) = ?

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 2}{300} = \dfrac{50 \times 1}{\text{T}$2} \\[1em] \text{T}2 = \dfrac{50\times 3}{2} \\[1em] \text{T}_2 = 75 \text{K} \\[1em]

∴ Final temperature of the gas = 75 - 273 = -198°C