A spherical air bubble is rising from the depth of a lake when pressure is P atm and temperature is T K. The percentage increase in its radius when it comes to the surface of a lake will be (Assume te

Question

A spherical air bubble is rising from the depth of a lake when pressure is P atm and temperature is T K. The percentage increase in its radius when it comes to the surface of a lake will be (Assume temperature and pressure at the surface to be respectively 2T K and P/4)

Prashant Kotian · Accepted Answer

Correct answer: A. using combined gas law: p1 × v1 / t1 = p2 × v2 / t2 → p × v1 / t = (p/4) × v2 / 2t → v1 = v2 / 8 → v2 = 8 × v1. since volume v ∝ r^3 → r2^3 = 8 × r1^3 → r2 = 2 × r1. percentage increase in radius = [(2r1 - r1)/r1] × 100 = 100%.

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