Chemistry - Ideal Gas Question with Solution | TestHub
A swimming pool (Figure) is conical in shape of diameter 20 m. To measure the depth of the pool, a pipe line having cross sectional area π mm2 has been introduced through the base centre to the depth of the pool. Other end of the pipe line is connected with the gas cylinder. When gases are passed through the pipe line, it has been measured that the volume of each bubble across the pipe line at the surface of the pool is 2π mm3. Assume the temperature of water is same as that of atmosphere and 1 atm pressure is equal to 10 m of water column. If the water holding capacity of the swimming pool is V m3, then the value of 3V/100π is
Answer:
Solution:
A bubble detaching from the pipe mouth is a sphere whose diameter equals the pipe bore. Cross-section π mm2 gives radius r = 1 mm, so bubble volume at the bottom Vb = (4/3)π(1)3 = 4π/3 mm3.
At the surface (1 atm) the bubble volume is 2π mm3. Isothermal Boyle law between bottom (depth h, pressure = 1 + h/10 atm) and surface:
(4π/3)(1 + h/10) = 2π x 1 ⇒ 1 + h/10 = 3/2 ⇒ h = 5 m.
Conical pool volume V = (1/3)π r2 h = (1/3)π(10)2(5) = 500π/3 m3.
3V/100π = 3 × (500π/3)/(100π) = 5.
