# Two rising bubbles of differing temperatures

Consider two bubbles rising through some medium (water, for example). Given that the two bubbles have the same initial size, pressure, and temperature but differing velocities, which bubble will be hotter/ have the greater increase in temperature after travelling the same distance and under what circumstances? Which will be larger?

For example, if we assume that the bubbles expand adiabatically, I'm torn between saying that the slower will be larger due to the lowered resistance of the surrounding medium or smaller due to the relatively smaller increase in internal energy.

This is my first stack post, so please let me know if this is an appropriate question.

• What makes you think the bubbles undergo a change in temperature? From what I gather, you only mention that the bubbles themselves have different velocities. A change in external energy doesn't mean a change in internal energy, which is what temperature is. May 4, 2016 at 18:37

this can be address by an isentropic process $$P^{\gamma -1}T^{-\gamma}=const$$

The bubble rising higher experience less hydraulic pressure and thus will be colder. Assuming the index is 1.4, rising 1 meter to the water surface, the hydraulic pressure will decrease by 9.8kPa. With atmospheric pressure on top of it, the pressure change ratio is 0.91. This will give temperature change ratio 0.970. Assuming the initial temperature is 10 degrees C, when the bubble reaches to the surface, the temperature will be 2.5 degrees C.