An air bubble of volume 1.0 cm³ 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 at a temperature of 35° C?

Solution

At the bottom of the lake,

Volume of air bubble, V = 1.0 cm³
Depth of lake = 40 m
$Pressure at the bottom of the lake, P_{B} = 40 m of H_{2} O + 1 atm = 40 \times 1000 \times 9.8 + 1.01 \times 10^{5} = 4.93 \times 10^{5} Pa$
Temperature, T = 12^o C = 12+273 K = 285 K

At the top of the lake

Volume of air bubble = ?
Changed temperature, T' = 35^o C
Pressure at the top of the lake, P_t= 1 atm = 1.01 $\times 10^{5}$ Pa

Volume at the top, V_t = ?

Now using the gas equation, we have

$\frac{P_{b} V_{b}}{T_{b}} = \frac{P_{t} V_{t}}{T_{t}} \Rightarrow V_{t} = \frac{P_{b}}{P_{t}} \frac{T_{t}}{T_{b}} V_{b} = \frac{4.93 \times 10^{5}}{1.01 \times 10^{5}} \times \frac{308}{285} \times 1 = 5.3 c m^{3}$

is the required volume of the air bubble at the surface.

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An air bubble of volume 1.0 cm³ 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 at a temperature of 35° C?

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Mechanical Properties Of Fluids

An air bubble of volume 1.0 cm3 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 at a temperature of 35° C?

Some More Questions From Mechanical Properties of Fluids Chapter

Can sound travel in vacuum?

Can two persons hear each other on the moon? Explain.

Can electromagnetic wave propagate in vacuum?

Can we listen in vacuum?

Which of the two moves forward during wave motion - particle or disturbance?

What type of wave is sound wave when it travels in air?

What type of wave is sound wave when it travels in solids?

Which of the two - sound or light is longitudinal in nature?

In what form the sound travels in air?

Define frequency.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

An air bubble of volume 1.0 cm³ 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 at a temperature of 35° C?