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Two identical bubbles of gas form at the bottom of a lake,
Chapter 1, Problem 38P(choose chapter or problem)
Problem 38P
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 it 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.
Questions & Answers
QUESTION:
Problem 38P
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 it 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.
ANSWER:
Solution 6P
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 it always remains in thermal equilibrium with the water (which has the same temperature everywhere).
It’s a simple example of adiabatic versus isothermal expansion of an ideal gas. Bubble A rises quickly so that no heat is exchanged with the surrounding water (adiabatic expansion), while bubble B rises slowly so that its temperature remains constant (isothermal expansion)
Bubble A experiences adiabatic expansion, so it obeys the relation
Bubble B experiences isothermal expansion, so it obeys the relation =