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AP Physics 2
9.4 The First Law of Thermodynamics
9.2 The Ideal Gas Law
IntermediateMCQProportional AnalysisConceptual24.9k
A vertical cross-section of water with a horizontal surface line at the top. Deep underwater near the bottom, a small circular air bubble is drawn and labeled with pressure 3P_0 and volume V_0. A vertical upward dashed arrow points from the lower bubble to a larger circular bubble near the top surface. The upper bubble is labeled with pressure P_0 and volume 2V_0. Atmospheric pressure above the water surface is labeled P_0. No other labels, lines, text, or axes appear.
An air bubble rising through water from depth to the surface.
A bubble containing a fixed amount of ideal gas is released deep underwater at a depth where the total pressure is \(3P_0\). As the bubble rises to the surface where the ambient pressure is \(P_0\), its volume expands from \(V_0\) to \(2V_0\) while absorbing thermal energy from the surrounding water.

OptionRatio \(\dfrac{T_f}{T_i}\)Internal Energy Change \(\Delta U\)
A\(\dfrac{3}{2}\)Positive
B\(\dfrac{2}{3}\)Negative
C\(\dfrac{2}{3}\)Positive
D\(6\)Positive

Which entry in the table correctly identifies the ratio of the final absolute temperature to initial absolute temperature, \(\dfrac{T_f}{T_i}\), and the sign of the change in internal energy, \(\Delta U\), of the gas in the bubble?

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