A gas bubble of volume 2 ~cm ^3 rises from the bottom of a pond of depth 10 m at 17^0 C . What will be the volume of the bubble when it reaches the surface of the pond? Atmospheric temperature is 27^ C and the pressure at the bottom of the pond is double that of the pressure at the surface.

Step-by-step solution

Let P₁ and V₁ be the pressure and volume at the bottom of the pond, and P₂ and V₂ be the pressure and volume at the surface. Given V₁ = 2 cm ^3 . The temperature at the bottom is T₁ = 17 + 273 = 290 K . The temperature at the surface is T₂ = 27 + 273 = 300 K . The pressure at the bottom is given as double the atmospheric pressure, so P₁ = 2P₂ . Using the ideal gas law in the form P₁ V₁ T₁ = P₂ V₂ T₂ , we substitute the known values: 2P₂ 2 290 = P₂ V₂ 300 Canceling P₂ from both sides: 4 290 = V₂ 300 V₂ = 4 300 290 =