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In this problem set I have a passage that describes an experiment that looks at the changing temperature as an air filled balloon rises to the surface from the bottom of a water filled tank. The graph they provide shows that as the balloon rises to the surface the temperature of the air in the balloon decreases. (I'm paraphrasing a lot of the question because it's long and has a bunch of information that's not pertinent such as dimensions of the tank, dimensions of a valve that's not even used in any problem!!! etc.)

I'm struggling with the idea of the temperature changing at all. From the answers from the problems it seems that the gas is doing work by expanding thereby losing internal energy and thus temperature. This to me makes sense, but I keep looking at the PV=nRT and thinking well wait, wouldn't the temperature just be fixed and the volume and pressure change correspondingly? Help getting through these basic concepts would be great!

Also one of the problems I struggled with:

Which of the following items of information would NOT help in predicting the results [shown in the graph]?

A) The number of air molecules inside the balloon

B) The thermal conductivity of the rubber (of the balloon)

C) The variation with depth in the speed of the balloon

D) The total mass of the water in the tank

Answer is D

I'm confused what the test makers were hinting at with C; if C could be included in your explanation of this experiment that would be great (does this somehow give the amount of internal energy lost??). I can't find other examples of this kind of experiment, is it a specific type? I.e. Does it have practical applications (even a name of like a standardized experiment similar to "pendulum motion" etc) or is it simply a conceptual check?

Thanks!

Update: http://s24.postimg.org/yzvb1ci5x/balloon_gas_temp_experiment.jpg

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Why would the temperature of the gas in the balloon be fixed? Note that it will depend, among other things, on the thermal conductivity of the rubber of the balloon: if the thermal conductivity were zero, the gas in the balloon would expand isentropically, rather than isothermally.

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The ideal gas equation you try to use for understanding does not provide a full description. To completely describe a thermodynamical system, you need the relevant thermodynamic potential, which here is the internal energy if I understood well your formulation (is a bit vague). Processes like the isobaric expansion occuring here, cannot be explained through this equation of state, nottice that the entropy $S$ is not involved, thus you don't fully describe your gas with it. You are right, in an isentropic expansion presion and volume vary, but this is a sudden process, while the kind of processes described with the equation of state involve "quasi-stationary and in contact with temperature reservoir" variation of the conditions. That is why C is relevant, since the more sudden is the rise, corrrespondingly faster will be the expansion and this impacts the heat transfer between the water and the gas (or the thermalization of the gas with the surroundings).

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