Question

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?

Answer 1

volume of bubble is 2.736 cm³

Step-by-step explanation:

given data

height h = 35 m

volume = 1.98 cm³ = 1.98 ×
`10^(-6)` 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 ×
`10^(5)` Pa and ρ density of water

put here value in equation 1

pressure = Pt + ρ × g × h

pressure = 1.013 ×
`10^(5)` + 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 ×
`10^(-6)` × 5.2 / ( 1.013 ×
`10^(5)` × 16.5 )

v2 = 2.736 ×
`10^(-6)` m³

so volume of bubble is 2.736 cm³