A thin tube, sealed at both ends, is 1.00 m long. It lies horizontally, the middle 10.0 cm containing mercury, and the two equal ends containing air at standard atmospheric pressure:

If the tube is now turned to a vertical position, by what amount will the mercury be displaced, if the process is adiabatic? For air γ = 1.40

Question

A thin tube, sealed at both ends, is 1.00 m long. It  lies horizontally, the middle 10.0 cm containing mercury, and the two equal ends containing air at standard atmospheric pressure:

If the tube is now turned to a vertical position, by what amount will the mercury be displaced, if the process is adiabatic?  For air γ = 1.40

anonymous · Answer

sealed, what is the temperature of the air.

anonymous · Answer

as well as the diameter of the tube.

anonymous · Answer

The temperature is not given as well as the diameter.

anonymous · Answer

so standard conditions are assumed then

anonymous · Answer

The mercury will drop until the weight of the mercury matches the pressure of the air in the tube.

anonymous · Answer

There is no any notion of it. But I think we are free to choose the temperature and the diameter cause whatever we choose it will cancel out eventually.

anonymous · Answer

Pressure = F/Area

anonymous · Answer

We are asked to calculate exact displacement of mercury from its initial position.

anonymous · Answer

F = mass of mercury * g

anonymous · Answer

Density = mass of mercury / V

anonymous · Answer

V = A * d

vincent-lyon.fr · Answer

Is the answer 2.1 cm ?

anonymous · Answer

Yes! But how did you find it?

vincent-lyon.fr · Answer

$pV^{\Large \gamma} = constant$

anonymous · Answer

Yes I know this formula but I stumbled upon that power thing when solving equation: $$(V _{0}+x)^{\gamma}/P _{0}+ P_{0}/7.6=(V _{0}-x)^{\gamma}/P _{0}$$ Where P _{0}] is 1 atm. pressure, x is displacement of mercury and V _{0} is 0.45 m * Pi*D/4
Or may be you have chosen another way of solving of this problem? Please, show me the way yo did that.

vincent-lyon.fr · Answer

I had to solve it numerically.

anonymous · Answer

Sorry x is difference in volume caused by displacement of mercury. Knowing it one can easily find displacement itself.

vincent-lyon.fr · Answer

Do not worry about volume. Cross-section of tube cancels out.

anonymous · Answer

Yes I know that, but I didn't get what you mean by numerical solving? You have  just chosen some numbers to put it in equation?

vincent-lyon.fr · Answer

Yes, find the root using a calculator or a spreadsheet.

anonymous · Answer

Oh, I see, I thought that there is a way of finding exact answer. Thank you very much!

vincent-lyon.fr · Answer

There would be a way if change was isothermal. I don't think there is one for adiabatic.