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# Nitrogen gas, calculate temperature change over time

## Nitrogen gas, calculate temperature change over time

(OP)
Hello all
I am currently working on designing a calculator that is able to calculate the temperature of nitrogen gas inside a container, as well as calculating the temperature on the container after some of the gas is "bled" off/out over a given time.

For now (as I am fairly new to thermodynamics),I am considering an ideal gas. And I find that T2 = T1 * (P2 / P1).

The problem I have is to evaluate how the temperature of the nitrogen gas is impacted by the material of the container, and also how the ambient temperature (outside the container, air) impacts the nitrogen gas temperature over time. An example is that a 50 liter container consist of nitrogen with a temperature of 313K with a pressure of 200Bar. For 120 seconds the pressure is reduced to 150bar. Calculate the temperature inside the container, and also the temperature of the container.

Any help and tips on how I should proceed with this problem is much appreciated.
-Arve

### RE: Nitrogen gas, calculate temperature change over time

Is this a student post / exam question? There's a separate forum for that.

But a hint here - Now you're including the container you need to think energy as well as ideal gas.

So this is impossible without knowing the mass of the container.

And then throw in some thermodynamics in terms of heat transfer between the gas and the container, both inside and outside the container.

In 2 minutes the temperature of the container doesn't have much time to react, so this is perhaps a bad example, or maybe means the temp of the container essentially stays the same? So your ideal gas law applies to the gas temp, which then slowly reverts to ambient temperature over say 15 -20 minutes? It doesn't make much difference here, but remember T is in K and pressure is absolute pressure.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: Nitrogen gas, calculate temperature change over time

(OP)
This might not be the correct forum for this question. I finished my bachelor degree 2 weeks ago, and this is one of the first projects I have.

It is the part of "thermodynamic in terms of heat transfer between the gas and the container, both inside and outside the container" I am struggling with.

Yes, the example of 2 minutes is not a good example. Lets say the pressure is bled from x to y, in a range of 60 minutes. Then I would imagine it would have an impact?

### RE: Nitrogen gas, calculate temperature change over time

The thing here is that you're dealing with transient events which don't lend themselves to calculation very easily.

Instant or steady system - yes

So if you plotted the temperature of the gas in say a 2 minute fall in pressure it would be nearly vertical.
The container temperature would be nearly flat as it has a much higher heat capacity than the gas, but then over time the container would reduce and the gas temp rise until near equilibrium then they would both rise together back to ambient if no more gas was being used.

If you bled it over 60 minutes, I doubt you would see more than a degree or three of temp drop because the heat input from the ambient air would match the heat loss from the gas.

Find a text book or do some research online - there's plenty free simple thermodynamics text books out there, but first work out what you want to know and why and also what level of accuracy do you want.

This is simple gas to surface convection heat transfer.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

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