An underwater bubble with a radius of 0.5 cm at the bottom of the tank, where the temperature is $5^{o} C$ and pressure is 3 atm rises to the surface, where the temperature is $25^{o} C$ and pressure is 1 atm. What will be the radius (in cm) of a bubble when it reaches to the surface?

Write numerical value (up to 2 digits only) after decimal point only as for 0.19, write 19).

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Solution

The mole of air contained in the bubble at the bottom of the tank as well as on the surface remains the same.

Thus, $n = \frac{P_{1} V_{1}}{R T_{1}} = \frac{P_{1} V_{2}}{R T_{2}}$

At the bottom of the tank At the surface

$\frac{3 \times (4 / 2) π \times (0.5)^{3}}{R \times 278} = \frac{1 \times (4 / 3) π r^{3}}{R \times 298}$

$r = 0.74 c m$

so answer is 74.

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The mole of air contained in the bubble at the bottom of the tank as well as on the surface remains the same.Thus, n=P1V1RT1=P1V2RT2At the bottom of the tank At the surface3×(4/2)π×(0.5)3R×278=1×(4/3)πr3R×298r=0.74cmso answer is 74.