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An air bubble was initially released from the bottom of an ocean. Assume that the air in the air bubble is an ideal gas and its temperature remains constant at 25 degrees Celsius. Is heat added or removed from the air bubble as the bubble rises?

My reasoning is that since total internal energy, $U \propto T$, the total internal energy must have remained constant. But from the laws of thermodynamics, $U = W + Q$. Since $pv = nRT$ remains constant, no work is done on the bubble and hence $W = 0$. It follows that $Q$ must be equals to $0$, i.e. heat is neither removed nor added to the air bubble.

Is my reasoning sound?

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If the air in the bubble is expanding, the gas should be doing work against the ocean, and the temperature should drop(in the case of adiabatic expansion). Since the temperature is said to remain constant, heat must be added to the bubble.

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  • $\begingroup$ If the air expands but its pressure drops at the same time, how can one deduce that work is done against the ocean? $\endgroup$ – Yiyuan Lee Jun 27 '14 at 12:43
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    $\begingroup$ Imagine the bubble is a cylinder pushing against a weighted cylinder. As the piston is pushed out, there is a force $P\cdot A$ on the piston, so when it moved a distance $dx$ the work done is $P\cdot A \cdot dx$. Integrate. Work done. $\endgroup$ – Floris Jun 27 '14 at 12:45
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    $\begingroup$ Awesome. You're a lifesaver. Cheers! $\endgroup$ – Yiyuan Lee Jun 27 '14 at 12:49

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