Beer Bubble Rises: Find Volume Ratio - 65 characters

In summary, a bubble rises from the bottom of a glass of beer to the top, with an air pressure of 1.01 X 10^5 Pa at the top. If the temperature and number of moles of CO2 remain constant, the ratio of the bubble's volume at the top to its volume at the bottom can be found by solving Boyle's law. The equation used is (PV)top = (PV)bottom, and the volume at the top is assumed to be 0.200m^3. The ratio of the pressures can be used to find the desired ratio of the volumes.
  • #1
colton4286
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A bubble, located 0.200 m beneath the surface in a glass of beer, rises to the top. The air pressure at the top is 1.01 X 10^5 Pa. Assume that the density of beer is the same as that of fresh water. If the temperature and number of moles of CO2 remain constant as the bubble rises, find the ratio of its volume at the top to that at the bottom.

What I did was use the equation [Pressure at bottom = Pressure at top + P("rho")*g*h]. Since n and T are constant, I know: (PV)top = (PV)bottom. I need one of the volume values to solve for the other (V at top or V at bottom). Is the volume at the top 0.200m^3? Thanks.
 
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  • #2
You just need the ratio, not the true value for the volumes. So just solve Boyle's law for the ratio of the pressures. . .

[tex] P_1 V_1 = P_2 V_2 [/tex]
 
  • #3


The volume ratio of the bubble at the top and bottom is 1.01 X 10^5 Pa / (1.01 X 10^5 Pa + 1000 kg/m^3 * 9.8 m/s^2 * 0.200 m) = 0.9998.
 

What is the purpose of the experiment?

The purpose of the experiment is to find the volume ratio of a beer bubble as it rises to the surface.

What materials are needed for this experiment?

The materials needed for this experiment include a glass of beer, a stopwatch, a ruler, and a calculator.

How is the volume ratio calculated?

The volume ratio is calculated by measuring the diameter of the beer bubble at different heights and using the formula V = (4/3)πr³, where V is the volume and r is the radius of the bubble.

Why is this experiment important?

This experiment can help us understand the behavior of bubbles in liquids and can have practical applications in industries such as brewing and food production.

What are the potential sources of error in this experiment?

Potential sources of error in this experiment include variations in bubble size, inaccuracies in measurement, and external factors such as temperature and air pressure.

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