# A gas is to be filled from a tank of capacity 10 000 liters into cylinders each having capacity of 10 litres. The condition of the gas in the tank is pressure inside the tank is 800 mm of Hg and temperature inside the tank is -3degree celcius. When the cylinder is filled, the pressure gauge reads 400 mm of Hg and temperature is 0degree celcius. Find the number of cylinders required to fill the gas

1
by Souvik1

2015-04-22T02:20:18+05:30

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V1 = 10,000 litres      P1 = 800 mm Hg          T1 = -3 °C = 270°K

Volume of a cylinder = 10 litres
Let there be n cylinders used to fill all the gas from the tank.
V2 = 10 * n  litres.      T2 = 0 °C = 273 °K      P2 = 400 mm Hg

The ideal gas law states that :
P1  V1 / T1  =  P2 V2 / T2
V2 =  P1 V1 T2 / (T1 P2)
= 800 * 10,000 * 273 / (270 * 400)
= 20, 222.22  litres
= 10 * n
n = 2, 022.22 cylinders
or  2, 023 cylinders  with the last  cylinder having less of the gas as compared to the other cylinders.