thermal properties question

[BSZDcZMX]

Hi there, I wanted to check whether I got this one correct:

 

Q: A bubble rises from a height [math]h[/math] from the bottom of a tall open tank of liquid that is at uniform temperature. Write an expression for the bubble's volume [math]V_{f}[/math] just before it bursts at the surface in terms of it's original volume [math]V_{i}[/math], and the uniform density of the liquid [math]\rho[/math].

 

A: By taking the temperature to be constant, the initial pressure to be that of the atmosphere plus the pressure at a height [math]h[/math] in the liquid and the final pressure to be simply that of the atmosphere. By using the [math]\frac{PV}{T} = constant[/math] equation I derive:

 

[math]\frac{P_{i}V_{i}}{T} = \frac{P_{f}V_{f}}{T}\rightarrow (P_{atm} + \rho gh)V_{i} = P_{atm}V_{f}\rightarrow V_{f} = \frac{P_{atm} + \rho gh}{P_{atm}}V_{i}[/math]

 

Is this correct?

 

Thanks

[BSZDcZMX]

No replies?

[CaptainPanic]

That looks correct to me.

[swansont]

It may be how the question is worded, but I wonder about the use of h. Because won't the bubble will burst when the top of the bubble reaches the surface, rather than the center of the bubble? But that may be overthinking the problem.

[CaptainPanic]

It may be how the question is worded, but I wonder about the use of h. Because won't the bubble will burst when the top of the bubble reaches the surface, rather than the center of the bubble? But that may be overthinking the problem.

Agreed. h seems to be defined as the bottom of the barrel. But I guess it's just the height of the tank, so then you would not have a problem.

 

As long as the bubble gets larger as it rises up, you're good to go!

[BSZDcZMX]

Hi guys, thanks for the replies!

 

Was sure it was correct!