An air bubble of 20 cm2 volume is at the bottom of a lake 40 meters deep where the temperature is 4-C- The bubble rises to the surface which is at a temperature of 20-C- Take the temperature to be the same as that of the surrounding water and find its volume just before it reaches the surface-

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Standard X

Physics

Ideal Gas Equation

An air bubble...

Question

An air bubble of 20 $c m^{2}$ volume is at the bottom of a lake 40 meters deep where the temperature is $4^{\circ} C$ . The bubble rises to the surface which is at a temperature of $20^{\circ} C$ . Take the temperature to be the same as that of the surrounding water and find its volume just before it reaches the surface.

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Solution

Let the atmospheric pressure be 1atm. Hence, at the bottom, the pressure will be

$P = 1.01 X 10^{5} + (1000) (10) (40) = 5.01 X 10^{5} P a$

Since $\frac{P V}{T}$ must remain constant,

Hence, $\frac{4.01 X 10^{5} X 20}{277} = \frac{1.01 X 10^{5} X V}{293}$

$V = 105 c m^{3}$

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