Study of Gas Laws — Question 15

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