Question

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

Answer 1

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.

Answer 2

Answer:Let the capacity of the cylinder be V

Since,Capacity of the cylinder V=10000 litres(Given)

Let original pressure  be P

P=800mm(Given)

Let original temperature be T

T=-3 degrees Celcius(Given)

Since,0 degree Celcius=273k

So,in Kelvin it will be-

=(-3)+273=270k

Let new Pressure be P1

P1=400 mm of Hg (Given)

Let new Temperature be T2

T2=0 degree Celcius

So,in Kelvin it will be-

=0+273=273k

Using gas equation

PV/T=P1V1/T1

=800*10000/270=400*V1/273

=20222.2litres

No. of cylinder=V1/Volume of one cylinder

=20222.2/10

=2022.22

Therefore,No. of cylinder=2022(Approax)

Explanation:The question could be easily solved.I have applied the gas equation because it is used for calculating changes in gas volume when both its pressure and temperature change.