# Pressure and Temp question

If you have a vessel that is rated for 500 psi at room temp how would you go about determining if it will fail if you do the following

fill it half way with water then pressurize to 200 psi and heat to 100F

i am trying to purchase a vessel for a project i am doing and i want to reassure myself i am getting the correct one

I was going to try

P1T2 =P2T1

with P1 = patm ,T1=room temp and T2=100F then solve for P2 and if it is less thsn 500 im
Is there a better way

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256bits
Gold Member
Have you looked at your equation/
Do pressure and temperature have an inverse relation to one another as your equation implies,

Or are they proportional to one another in some way.
Take another look at the ideal gas law.

Which does not completely apply here, but you should get your first principles sorted out so if and when you do get an answer you can be more confident that it all makes sense.

I went on wikipedia and under Gay - Lussac's Law they had:

P1/T1 = P2/T2

Which if you rearrange you would have

P1T2 = P2T1

256bits
Gold Member
Oh sorry. My apologies. I did not read the subscripts correctly.

No worries. If this eqn does not totally apply what would be a more appropriate way to spproach this

256bits
Gold Member
Your equation comes from the ideal gas law - ie PV = nRT
With a constant volume V and mass of gas ( represented by n, moles ), then P/T = C ( a constant )

The ideal gas law is applicable for an ideal gas, which at normal pressures and temperatures that we normally see, encompases just about all gases.

The temperature for T is either the Kelvin or the Rankine temperature, so one has to convert Celcius or Fahrenheit to that scale.

You can do a calculation based on that to see what you get as a final temperature, if you heat the water (and water vapour ) from whatever initial temperature you started from.

BUT, if the volume contains a mixture of liquid and vapour, in this case water and steam, then as you heat the water more water will turn into vapour. The vapour pressure of water increases with increasing temperature.

Wiki here gives a brief description and a table of vapour pressure of water versus temperature from 0C to 100C. You can see that at 100C the vapour pressure of water equals the atmospheric pressure. And that explains why water will boil at 100C if subjected to atmospheric pressure.
http://en.wikipedia.org/wiki/Vapour_pressure_of_water

So in your case you have a mixture of water vapour and air in avessel pressurized to 200 psi, of which the water at the initial temperature is contributing its vapour pressure. Heating will now expand the air and also produce more steam at a higher water vapour pressure. Both together will give the final pressure.

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Ideal gas equation is applicable only for gases at low pressure and density. water and steam cannot be considered as ideal gases. You have to use property tables of saturated water and steam for this problem.