Question

An air bubble of volume 1 cm³ rises from the bottom of a lake 40m deep to the surface at a temperature of 12°C. The atmospheric pressure is 1 x 10⁵ Pa, the density of water is 1000 kg/m³ and g = 10m/s². There is no difference of the temperature of water at the depth of 40m and on the surface. The volume of air bubble when it reaches the surface will be

(1) 5 cm³

(2) 2 cm³

(3) 4 cm³

(4) 3 cm³

Answer 1

Correct option is (1) 5 cm³

P = P₀ + ρgh = 10⁵ Pa + 10³ × 10 × 40 = 5 × 10⁵ Pa

At T is constant

PV = P₀V₀

⇒ 5 x 10⁵ Pa × 1cm³ = 10⁵ Pa x V₀ 

⇒ V₀ = 5cm³