Air bubble at the bottom of a lake 35.0 m deep has a volume of 1.98 cm3. part a if the temperature at the bottom is 5.2 ∘c and at the top 16.5 ∘c, what is the volume of the bubble just before it reaches the surface?

volume of bubble is 2.736 cm³

Explanation:

given data

height h = 35 m

volume = 1.98 cm³ = 1.98 × m³

temperature t1 = 5.2°C

temperature t2 =  16.5°C

to find out

volume of the bubble

solution

first we find pressure depth  35 m

pressure = Pt + ρ × g × h    ................1

here Pt is pressure at top = 1.013 × Pa and  ρ density of water

put here value in equation 1

pressure = Pt + ρ × g × h

pressure = 1.013 × + 1000 × 9.8 × 35

pressure =  444300 Pa

so

from gas equation

p1×v1 / t1  = pt×v2 / t2

put here value

v2 = p1×v1×t1  / pt×t1

v2 = 444300× 1.98 ×  × 5.2  / ( 1.013 × × 16.5 )

v2 = 2.736 × m³

so volume of bubble is 2.736 cm³

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