Question

An air bubble of volume 1.0 cm³ rises from the bottom of a lake 40 m deep at a temperature of 12°C. To what volume does it grow when it reached the surface, which is at a temperature of 35°C?

Answer 1

Volume of the bubble inside,

V₁ = 1 cm³ = 1 x 10^-6 m³

Pressure on the bubble = Pressure of water + atmosphere pressure,

= ρgh + 1.01 x 10⁵

= 1000 x 9.8 x 40 + 1.1 x 10⁵ = 3.92 x 10⁵ + 1.01 x 10⁵

= 4.93 x 10⁵ Pa

Temperature, T₁ = 12°C = 273 + 12 = 285 K

Also, Pressure outside the lake

p₂ = 1.01 x 10⁵ Nm^-2

Temperature, T₂ = 35° = 35 + 273 = 308 K

Volume, v₂ = ?

Now, p₁V₁/T₁ = p₂V₂/T₂

or, V₂ = p₁V₁/T₁ x T₂/p₂

= {4.93 x 10⁵ x 1 x 10^-6 x 308}/{285 x 1.01 x 10⁵}

= 5.3 x 10^-6 m³