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Question
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:
- The pressure inside the tank is 800 mm of Hg.
- The 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.
Solution
V1 = 10,000 L
P1 = 800 mm of Hg
P2 = 400 mm of Hg
T1 = −3°C + 273 = 270 K
T2 = 270 K
V2 = ?
Applying the gas equation,
`("P"_1"V"_1)/"T"_1 = ("P"_2"V"_2)/"T"_2`
V2 = `("P"_1"V"_1)/"P"_2`
= `(800 xx 10,000 "L")/(400)`
= 20,000 L
Number of cylinders = `"V"_2/"Volume of one cylinder"`
= `(20,000)/10`
= 2000 cylinders
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