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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explanation:

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.