# Pressure drop as volume changes

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## Main Question or Discussion Point

I am trying to calculate pressure losses. I've attached an image to show what I mean. Starting out tank 1 is 92.8 litres at 155 psi and when the shutoff valve is open the volume goes from 92.8 to 192.8 and so I thought the pressure would drop by the same factor that the volume increased by so giving 74.59 psi in each tank (192.8/92.8=2.078 so 155/2.078=74.59). This is then fed into a larger tank and using the same method as before I worked out the pressure would be 17.63 psi. Is this the correct way to calculate pressure changes?

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## Answers and Replies

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Chestermiller
Mentor
Are the tanks allowed to thermally equilibrate with the room before they are separated? Or is the transfer made, and then the temperatures re-equilibrate with the room? Or are the tanks insulated so well that they don't ever re-equilibrate thermally with the room?

If the thermal equilibration occurs before the tanks are separated, then the final pressures can easily be calculated using the ideal gas law.

The tanks haven't yet been positioned but the aim would be to position them next to each other. The aim is to conserve some air that would be otherwise be wasted so that it can be used to inflate a tyre. I hadn't really considered how temperature could affect this. Would it be better to allow the temperature to equal out before the valve is closed or close the valve and have each tank equal out themselves?

Chestermiller
Mentor
The tanks haven't yet been positioned but the aim would be to position them next to each other. The aim is to conserve some air that would be otherwise be wasted so that it can be used to inflate a tyre. I hadn't really considered how temperature could affect this. Would it be better to allow the temperature to equal out before the valve is closed or close the valve and have each tank equal out themselves?
I'm assuming that the tanks are at the same temperature (say 20 C) before the valve is opened. As the gas transfers, depending on whether the tanks are insulated or not (and how quickly the transfer takes place), the temperatures in both tanks can change. And they could continue to change after the valve is closed. So, are the tanks insulated? And, if they are not, are you going to wait until the temperatures equilibrate with the room before you close the valve again?

The tanks are not insulated. Would there be a way to calculate the time for the tanks to equal out temperature?

Chestermiller
Mentor
The tanks are not insulated. Would there be a way to calculate the time for the tanks to equal out temperature?
Yes. But first, let's assume that enough time is allowed for the temperatures to equilibrate with the room while the valve is still open. Okay? If so, are you familiar with the ideal gas law and how it would apply to this system? (I assume the pressures you indicate are gauge pressures, correct?)

Yes I'm working with gauge pressure. I haven't used the ideal gas law in a few years and so I may need some help applying it but am looking into it now.

Chestermiller
Mentor
It looks like the numbers in your figure were calculated using the ideal gas law, assuming constant temperature.