- #1
Jeann25
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Homework Statement
Two identical bubbles of gas form at the bottom of a lake, then rise to the surface. Because the pressure is much lower at the surface than at the bottom, both bubbles expand as they rise. However, bubble A rises very quickly, so that no heat is exchanged between it and the water. Meanwhile, bubble B rises slowly (impeded by a tangle of seaweed), so that is always remains in thermal equilibrium with the water (which has the same temperature everywhere). Which of the two bubbles is larger by the time they reach the surface? Explain your reasoning fully.
Homework Equations
isothermic -> W=NkT ln(Vf/Vi)
adiabatic -> VfTf^f/2=ViTi^f/2
(side question: What program do you use, or how do you make the typed out equations more readable?)
The Attempt at a Solution
I know that for isothermal, Q is positive because it's an expansion, and that W is negative because the volume is increasing.
For adiabatic, Q=0, and ΔU=W, and W is negative, so ΔU is negative. And I know that U is proportional to T, so ΔT is negative.
I'm not sure where to go from there. I tried substitution with this, since I know Vi is equal for both bubbles. So I tried solving for Vi for one, and substituting this in for the other, and seeing how the values were influenced. But that didn't seem to really help in any way. I'm having trouble doing this conceptually as well. I need some help on where to start.