So, using your arsenal of GEN Chem and Physics conceptual knowledge, Why does a bubble grow and move faster as it ascends to the top?
- A) Boyle's Law. Pressure of a gas is inversely proportional
to volume. Thus, when a bubble gains more CO2 molecules
it gains in volume, and thus decreases pressure. Pressure
equilibates to the top since top of the glass has a lower
pressure than at the bottom of the glass. Therefore,
sum of the net forces move it up.
B) Density. density of CO2 gas is lighter than Beer thus it rises
to the top.
C) Archimedes Principle. The bubble at the bottom of the glass
acts as a nucleation site, thus CO2 accumulates. As the bubble
grows bigger, it displaces more surrounding fluid. Therefore,
buoyancy increases and this net force moves it up.
D) Bernoullli's equation. P + 1/2 pv2 + pgy= constant. Since,
pressure is highest at the bottom of the glass, the velocity
of the gas molecules must be lower at the bottom of the
glass, therefore it rises to the top.
Choice A: This choice can be tossed out, because the author has changed laws midway through the explanation. The phrase "gains more CO
2 molecules" refers to Avogadro's law, and not Boyle's law, so using MCAT logic, this answer should be tossed out because it is factually incorrect. Answers that make logical sense but have mis-information can be incredibly tempting. This is an excellent wrong answer choice.
Choice B: This choice can also be tossed out because of the wording. Density refers to mass per volume, while "lighter" refers to weight, which depends on mass and acceleration due to gravity. Assuming the change in gravity from bottom to top of the beer glass is trivial (as would be the case in a normal glass), then lighter directly refers to mass. The mass of CO2 does not change as it rises, only it's volume changes. So this choice is eliminated because of non-correlating terminology.
Choice C: Choice C is a very true statement, and it explains the gradual growth of the bubble at the base of the glass. This same principle can be seen when boiling water. Water vapor forms aggregates on the base of the pan until the buoyant force on the bubble exceeds its weight and it breaks free. However, that very true statement does not explain the phenomenon in the question. The question centers on why it increaes its speed as it rises. This is another excellent case of a true, but irrelevant answer.
Choice D: Choice D is also tempting in that it alludes to a true concept, but it is also not applicable to this situation. Bernoullli's equation could be used to explain why the beer would flow out of a small hole in the base of the bottle at a gradually decreasing rate, but it neither explains nor refutes the rising of a bubble in and of itself.
Hence, I have no idea what to pick. If the question is why the bubble grows, choice
C is a must. It doesn't explain why it accelerates up, but it's the best answer.
This is a great question, because the best reasoning is a little piece of a couple of the answers. The bubble grows at the base of the bottle until it reaches a point where the buoyant force overcomes the weight and any applicable resistive forces (such as beerostatic force from the column of beer). Once the bubble breaks free of the base it may rise. As the bubble rises, Boyle's law comes into play. The bubble itself may or may not pick up other CO
2 molecules upon ascent (random chance says a few will collide and dissolve into it during its ascent). As the beerostatic pressure decreases (caused by the decrease in the weight of beer above the bubble as it rises), the external pressure decreases, resulting in an expanding bubble. This can be seen with any type of bubble released from some depth below the surface of a liquid. Fish tanks and scuba diving offer great examples of cases where bubbles grow as they ascend. As the bubble expands, it's buoyant force increases but its weight does not change, so it feels a greater net force upward. However, as is the case of anything moving through a medium, drag force also increases with increasing velocity. Because the cross-sectional area of the bubble increases, the drag is further increased. As such, the bubble is being accelerated upward, but how the acceleration increases upon ascent is open to debate without knowing the exact viscosity of the fluid, compliance of the bubble, and ideality of CO
2 at the given temperature.
So, basically, the only conslusion to be reached is that
you should drink it before all of the CO2 bubbles escape and it doesn't taste as good.
