Chemistry - Ideal Gas Question with Solution | TestHub
A water reservoir (Figure) is conical in shape of diameter 10 m. To measure the depth of the reservoir, a pipe line having cross sectional area π mm² has been introduced through the base centre to the depth of the reservoir. Other end of the pipe line is connected with a gas cylinder. When gas is passed through the pipe line, the volume of each bubble across the pipe line at the surface of the reservoir is 8.8π/3 mm³. Assume the temperature of water is the same as that of the atmosphere and 1 atm pressure equals 10 m of water column. If the water holding capacity of the reservoir is V m³, then the value of 3V/100π is
Answer:
Solution:
Pipe cross-section π mm² gives bubble radius r = 1 mm, so bubble volume at the bottom Vb = (4/3)π(1)³ = 4π/3 mm³.
Boyle's law between bottom (pressure 1 + h/10 atm) and surface (1 atm):
(4π/3)(1 + h/10) = 8.8π/3 ⇒ 1 + h/10 = 2.2 ⇒ h = 12 m.
Conical volume V = (1/3)π(5)²(12) = 100π m³.
3V/100π = 3 × 100π/(100π) = 3.
