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 follwos:
(a) Pressure inside the tank is 800 mm of Hg.
(b) temperature inside the tank is - $3^{\circ} C .$
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.

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Solution

Step 1:
Convert the pressure values

P1=800/760 =1.05 atm,

P2 =400/7460=0.525 atm,

T1=-3°C +273 = 270K ,

T2=270K,

V1=10000L,

V2=?

Temperature is same (constant), so it is related to Boyle's gas law.

$P 1 \times V 1 = P 2 \times V 2$

$V 2 = \frac{P 1 V 1}{P 2}$
= $\frac{1.05 a t m \times 10000 L}{0.525 a t m}$ = 20 000 Liters.
Step 2: Find the number of cylinders

Number of Cylinders = $20000 L \times \frac{1 c y l i n d e r}{10 L}$ = 2000 cylinders.

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