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 reaches the surface, which is of a temperature of 35 °C

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 reaches the surface, which is of a temperature of 35 °C (A) 10.6 × 10-6 m3 (B) 5.3 × 10-6 m3 (C) 2.8 × 10-6 m3 (D) 15.6 × 10-6 m3

Tardigrade Admin · Accepted Answer

Using, P1 =P2 + ρ gh Here, P2 = 1.013 × 105 atm, h = 40 m ρ = 103 kg m-3 (density of water), g = 9.8 m s-2 ∴ P1 = 1.013 × 105 + 103 × 9.8 × 40 = 493300 Pa Now, (P1V1/T1) = (P2V2/T2) Here, T1 = (12 + 273) = 285 K, T2 = (35 + 273) = 308 K, V1 = 1 × 10-6 m3 V2 is the volume of the air bubble when it reaches the surface ∴ V2 = (P1V1T2/T1P2) = ((493300 × 1 × 10-6)/285 × 1.013 × 105) × 308 = 5.26 × 10-6 m3 = 5.3 × 10-6 m3

Q. An air bubble of volume $1.0 c m^{3}$ rises from the bottom of a lake $40 m$ deep at a temperature of $12^{\circ} C$ . To what volume does it grow when it reaches the surface, which is of a temperature of $35^{\circ} C$

$10.6 \times 1 0^{- 6} m^{3}$

$5.3 \times 1 0^{- 6} m^{3}$

$2.8 \times 1 0^{- 6} m^{3}$

$15.6 \times 1 0^{- 6} m^{3}$

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

10.6×10−6m3

5.3×10−6m3

2.8×10−6m3

15.6×10−6m3

Q. An air bubble of volume $1.0 c m^{3}$ rises from the bottom of a lake $40 m$ deep at a temperature of $12^{\circ} C$ . To what volume does it grow when it reaches the surface, which is of a temperature of $35^{\circ} C$

$10.6 \times 1 0^{- 6} m^{3}$

$5.3 \times 1 0^{- 6} m^{3}$

$2.8 \times 1 0^{- 6} m^{3}$

$15.6 \times 1 0^{- 6} m^{3}$