A gas is to be filled from a tank of capacity 10,000 litres into cylinders each having capacity of 10 litres. The condition of the gas in the tank is as follows:

(a) pressure inside the tank is 800 mm of Hg.

(b) temperature inside the tank is -3°C.

When the cylinder is filled, the pressure gauge reads 400 mm of Hg and the temperature is 270 K. Find the number of cylinders required to fill the gas.

Initial conditions :

P₁ = Initial pressure of the gas = 800 mm of Hg

V₁ = Initial volume of the gas = 10,000 litres

T₁ = Initial temperature of the gas = -3°C = -3 + 273 = 270 K

Final conditions:

P₂ (Final pressure) = 400 mm of Hg

V₂ (Final volume) = 10 litres x n cylinders

T₂ (Final temperature) = 270 K

where n is the number of cylinders = ?

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 :

$\dfrac{800 \times 10,000}{270} = \dfrac{400 \times 10 \times n}{270} \\[1em] \text{n} = \dfrac{800 \times 10,000 \times 270}{400 \times 10 \times 270} \\[1em] \text{n} = \dfrac{800\times 10}{4} \\[1em] \text{n} = 2000 \\[1em]$

∴ Number of cylinders = 2000.