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Pressure in a Sphere?

04/07/2020 2:03 PM

I wonder if an excel sheet could be made for this.

Take a volume of a sphere, say 100 cuft.

it is equal air pressure in and out.

Now if you put into it 1 more cuft of outside air, what is the pressure differential?

put in 50 cuft

put in 100 cuft

Think a excel sheet could be made to do this calculation?

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#1

Re: Pressure in a sphere?

04/07/2020 2:55 PM

This may get you started on your quest for learning.

If however,you want a cut-and-paste solution,I will not be helpful.

http://www.ar.cc.mn.us/chemistry/Chem1061/Labs/GasLaws/GasLaws-vm.pdf

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#2

Re: Pressure in a sphere?

04/07/2020 3:11 PM
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#3

Re: Pressure in a sphere?

04/07/2020 5:14 PM

If temp is constant, each added volume of V raises the gauge pressure by 0.1469 V psi.

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#4

Re: Pressure in a sphere?

04/07/2020 9:01 PM

Given constant volume (V), pressure (P) in your sphere is proportional to the product of the amount of gas inside (nR) and the temperature (T).

PV=nRT or P=nRT/V

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#5

Re: Pressure in a sphere?

04/07/2020 11:52 PM

In answer to the original question, yes, of course it can. If the question can be put into a formula, and if a set of parameters are supplied, then an if-then statement can be used in Excel to read in each set of parameters, apply the formula, and output the result. The final result of all of this is a table of data. So again, yes, of course it can.

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#6

Re: Pressure in a sphere?

04/07/2020 11:55 PM

The way I thought of the problem was to consider the initial volume plus the added volume as the starting point and then calculated what the change in pressure would be assuming 14.7 psi atmospheric pressure initially and then calculate the increased pressure reducing the volume to in initial volume and then subtracting the initial atmospheric pressure: Below is how I arranged the problem in Excel:

Initial Volume (cu-??)Added Volume (cu-??)Initial Pressure 14.7 (psi) atmosphericPressure increase: ((B3+C3)*D3/B3)-D3 psi
100114.70.1470

You can change the initial and added volumes or even the initial pressure and get the change in pressure in the container you're using. Of course this assumes no change in temperature. Being somewhat lazy I try to avoid the nRT calculation because I have to look up too many things; for instance if you added a gas other than air you would then have to do the calculations using the nRT thing to take both gases into account.

Hope this helps...

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#7

Re: Pressure in a sphere?

04/08/2020 5:00 AM

From physics textbooks the excess pressure in a bubble is 2 times the surface tension divided by the radius. For something other than a bubble, the tensile properties of the material containing the gas can be substituted for the surface tension criterion. One must take into account that putting more gas into a fixed volume increases its temperature as well as the pressure according to the characteristics of the particular gas or mixture of gases. The properties of the containing material will vary with temperature as well.

Of course <...excel...> can do the calculation, as can a pocket calculator, a slide rule, a set of log tables or manual arithmetic! However, getting the mathematical model of the physical conditions right is fundamental to avoid GIGO, whatever calculabe is eventually employed.

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#8
In reply to #7

Re: Pressure in a sphere?

04/08/2020 8:27 AM

...and throw in the effect the removal of air from outside the vessel has on the external pressure.....and being ultra fussy any heat flow across the walls to equalize temperature...

PV = NRT is near enough for me.....confirming #2, #3 and #4

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#9
In reply to #8

Re: Pressure in a sphere?

04/08/2020 8:28 AM

Quite.

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