Physics · Pressure due to a fluid column, Pascal's law and its applications, effect of gravity on fluid pressure
An inverted vessel (bell) lying at the bottom of a lake, deep has of air trapped
An inverted vessel (bell) lying at the bottom of a lake, \( 50.6 \mathrm{m} \) deep has \( 50 \mathrm{cc} \) of air trapped in it. The bell is brought to the surface of lake. The volume of the trapped air will now be
- A. 200 ç
- B. 250 cc
- C. 300 cc
- D. 350 cc
Step-by-step solution
Using Boyle's law, P1V1 = P2V2. At bottom depth 50.6 m, pressure P1 = atmospheric pressure (1.013e5 Pa) + water pressure (ρgh = 1000*9.8*50.6 ≈ 4.96e5 Pa) = 5.97e5 Pa. At surface, P2 = 1.013e5 Pa. Initial volume V1 = 50 cc. Thus V2 = V1 * P1/P2 = 50 * (5.97/1.013) ≈ 294.7 cc, which rounds to 300 cc.
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