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# PV = NRT

05/31/2017 10:00 AM

We are amplifying our air system for an aplication from 100 PSI to 200PSI. How would i determine the temperature of the 200 PSI? Is it as simple as P1/T1+P2/T2?

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#1

### Re: PV=NRT

05/31/2017 10:15 AM

No, it is not as simple as you would like. The universal gas law has five attributes on either side of the equation. One is a constant and the other four are all variables. Your math not only ignores the other two variables it omits the operator of an equation sign.

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#2

### Re: PV=NRT

05/31/2017 10:31 AM

I meant P1/t1=P2/T2. How would i find the increase in temp then. I am not sure of volume

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#5

### Re: PV=NRT

05/31/2017 10:47 AM

If you're not sure of either the volume of gas or the moles of gas then you cannot predict the temperature.

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#21

### Re: PV=NRT

06/02/2017 5:33 PM

P1 x V1/T1 = P2 x V2/T2 is better to explain the problem you have.

V and T depend on each other. It is like saying A + B = 12, what is A?

The adiabatic compression formulas given above are better, but your 200 psi is the pressure in the tank when the pump stops - unless 200 psi is the minimum - in which case what is the highest pressure? - and if 200 psi is the cut-out pressure when the pump stops - what is the cut-in pressure when it starts?

The actual pressure during pumping will be the same as the tank pressure as it rises to 200 psi, or whatever.

the lower working pressures (whatever they happen to be at the time) are the ones to use in your formula.

If the booster is an air operated pump, then it is likely to slow down as pressure rises (it could go so slow as to stall) so adiabatic compression is unlikely in practice.

Booster pump suppliers could give you some practical working temperatures.

Most important is the pressure safety aspect as others have said

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#3

### Re: PV=NRT

05/31/2017 10:35 AM

Temperature at what point in the system?

Off the compressor?

In the tank?

Some place else?

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#4

### Re: PV=NRT

05/31/2017 10:40 AM

I am guessing the highest temperature point would be during compression from 100PSI to 200PSI.

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#9

### Re: PV=NRT

05/31/2017 11:15 AM

That sounds like a good guess. Remember that after this point your "hot" gas will be transferring this heat to any cooler surfaces containing this gas by the laws of thermodynamics.

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#6

### Re: PV=NRT

05/31/2017 10:54 AM

"We are amplifying our air system for an aplication"

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#8

### Re: PV=NRT

05/31/2017 10:58 AM

So we currently have 100 PSI throughout our plant. We need 200 PSI in order to run our valve gate system in our injection molds. So we have a booster pump that pumps up a tank to 200PSI. When the gates need opened or closed the pressure is released from the 200PSI tank and then is built up again by the booster pump.

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#10

### Re: PV=NRT

05/31/2017 11:50 AM

Well given that the air in the 200 PSI tank and system will be a few degrees above the ambient temperature while the compressor is running and for a few minutes after that as they cool down back to ambient temperature.

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#12

### Re: PV=NRT

05/31/2017 11:56 AM

I have supplied boosters for the application you describe and the temperature of the boosted air has never been a problem. It is cooling whilst in the tank. I would want to ensure that the components are capable of a working pressure of 200 psi as most are 150 psi (10 Bar) rated.

Best regards,

John

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#13

### Re: PV=NRT

05/31/2017 12:46 PM

That activity would be of great interest to the company that supplies burst indemnity insurance cover for the facility.

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#15

### Re: PV=NRT

05/31/2017 2:17 PM

OK, what happens when you pump air into a tank can be modeled as adiabatic compression. Two things will happen: the pressure will increase and the temperature will increase. How much temperature rise depends on the ratio of the specific heats for constant pressure and constant volume.

Adiabatic compression is the limiting case where no heat is allowed to escape, and it will give you the worst case for temperature rise.

Here is an example. You can plug in your values for 100 psi and 200 psi.

The compression stroke in a gasoline engine can be used as an example of adiabatic compression. The model assumptions are: the uncompressed volume of the cylinder is one litre (1 l = 1000 cm3 = 0.001 m3 ); the gas within is the air consisting of molecular nitrogen and oxygen only (thus a diatomic gas with five degrees of freedom and so γ = 7/5); the compression ratio of the engine is 10:1 (that is, the 1 l volume of uncompressed gas is reduced to 0.1 l by the piston); and the uncompressed gas is at approximately room temperature and pressure (a warm room temperature of ~27 °C or 300 K, and a pressure of 1 bar = 100 kPa, i.e. typical sea-level atmospheric pressure).

so our adiabatic constant for this example is about 6.31 Pa m4.2.

The gas is now compressed to a 0.1 l (0.0001 m3) volume (we will assume this happens quickly enough that no heat can enter or leave the gas through the walls). The adiabatic constant remains the same, but with the resulting pressure unknown

so solving for P:

or 25.1 bar. Note that this pressure increase is more than a simple 10:1 compression ratio would indicate; this is because the gas is not only compressed, but the work done to compress the gas also increases its internal energy which manifests itself by a rise in the gas's temperature and an additional rise in pressure above what would result from a simplistic calculation of 10 times the original pressure.

We can solve for the temperature of the compressed gas in the engine cylinder as well, using the ideal gas law, PV=nRT (n is amount of gas in mol and R the gas constant for that gas). Our initial conditions being 100 kPa of pressure, 1 l volume, and 300 K of temperature, our experimental constant (=nR) is:

We know the compressed gas has V = 0.1 l and P = 2.51×106 Pa, so we can solve for temperature:

That is a final temperature of 753 K, or 479 °C, or 896 °F, well above the ignition point of many fuels. This is why a high-compression engine requires fuels specially formulated to not self-ignite (which would cause engine knocking when operated under these conditions of temperature and pressure), or that a supercharger with an intercooler to provide a pressure boost but with a lower temperature rise would be advantageous. A diesel engine operates under even more extreme conditions, with compression ratios of 20:1 or more being typical, in order to provide a very high gas temperature which ensures immediate ignition of the injected fuel."

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#16

### Re: PV=NRT

05/31/2017 2:40 PM

Actually, this document is a more straight forward example for Adiabatic heat rise from compression. You can plug in 100 psi and 200 psi.

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#7

### Re: PV=NRT

05/31/2017 10:57 AM

P is pressure, V is volume, n is the number of moles of gas, R is the universal gas constant and T is absolute temperature (degrees Kelvin). You have four variables, P, V, n, and T. If you know any three, you can find the fourth.

I'm not sure what "amplifying the air system" means.

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#11

### Re: PV=NRT

05/31/2017 11:52 AM

PV=nRT is not Avogadro's Law (which is V/n=k), it is the Ideal Gas Law.

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#14

### Re: PV=NRT

05/31/2017 1:41 PM

Yup!

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#17

### Re: PV=NRT

05/31/2017 2:56 PM

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#18

### Re: PV = NRT

05/31/2017 7:55 PM

FWIW, way back in my tech college days I had an applied pneumatics class and one of the convenient rules of thumb for air compressor outlet temperature was on the rough order of 2 degrees F, or a bit less, per PSI over inlet temperature.

That was to say that if you had a air compressor putting out 150 PSI to a system with a 70 degree F inlet temperature if the outlet temperature was anything around or under, 70 + 150 x 2 = 370 F it was probably working okay.

I've checked many an air compressor with an IR thermometer and found that rule seems pretty consistent. Most run less and very few that are working right run higher unless they are being overdriven for their design or have a valve problem.

Given that I would expect you compressor outlet temperature to be about 200 F, or a bit under, whatever the inlet temperature is at most.

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#19

### Re: PV = NRT

06/01/2017 12:14 AM

Whilst all the comments seem valid, the temperate is measured from absolute zero, plus 460 + 32 for f or plus 273 for c. So you would need a huge difference in temperature make a significant difference overall.

Think I got that right.

Tony

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#20

### Re: PV = NRT

06/01/2017 11:53 AM

PV=nRT is applicable to the instantaneous temperature of the compresed gas. The temperature of system components will depend on time, area, conductivity, convectivity, etc. and will take a lot of detailed modeling to determine.

Of greater concern immediately is whether the increased pressure may lead to an unsafe condition due to potential dieseling of the compressor. If your compressor is actually running single stage at a 13:1 ratio and the air contains any oil, the flash point of the oil could result in diesel ignition of the air/oil mix or possibly carbonizing and leaving hard carbon deposits in the compressor cylinder, piston and valves. If two stage, you may need to add an intercooler between stages or switching to a high temperature oil.

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