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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.
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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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