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Pressure rise in closed system.?
2

Pressure rise in closed system.?

Pressure rise in closed system.?

(OP)
Hello Guys,

This should be an easy one; I have a hermetic closed system with 20ccm3 water at 20C. Now I add heat until it reaches 90C, what is the pressure? What if the temperature reaches 120C..?

Thanks in advance!

RE: Pressure rise in closed system.?

You must specify the initial pressure.  Also, does the volume remain constant? AND  is water the only component?

Regards

RE: Pressure rise in closed system.?

(OP)
Yes, sorry. The initial pressure is 1 atm. The volume remains constant eg. it is a rigid non flexible container and yes, water is the only component.

RE: Pressure rise in closed system.?

Using the Keenan-Keyes-Hill-Moore (KKHM) steam table formulation for water, I approximate the spec vol at 20C, 1 atm at about
1.00172(10^-3)m^3/kg

with that const spec vol, my forumulation yields

20C     0.14MPa    which I approximate as one atm.
70C     49.5MPa
90C     79.3MPa
120     130.5 MPa

The KKHM formulation for properties are based on input of v and t.  Therefore, I had to iterate to come up with the approximate specific volume.

Regards

RE: Pressure rise in closed system.?

Sailoday28,
I've always used the rule of thumb "about 100 psi change for every degree farenheit".  From your table, the actual relationship doesn't look quite that linear, but for figuring if things will break it still looks ok.

David

David Simpson, PE
MuleShoe Engineering
www.muleshoe-eng.com
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RE: Pressure rise in closed system.?


For liquids packed in rigid containers the developed pressure could be approximated by dividing the cubic thermal expansion α=(1/V)(∂ V/∂T)P by the isothermal compressibility κ=(1/V)(∂ V/∂ P)T. An example for water at 30oC:

(0.302×10-3/oC)÷(4.475×10-4/MPa) = 0.67 MPa/oC or about 6.7 bar/oC

The results are not linear because α increases while κ decreases with rising temperatures.

RE: Pressure rise in closed system.?

(OP)
Thanks for the quick replys. This give me a fair view of the situation. :)

RE: Pressure rise in closed system.?


Ferlev, please note that what I said for the temperature effects applies to water. With other liquids, temperature increases generally result in a rise of both the thermal expansion and the compressibility.

RE: Pressure rise in closed system.?

(OP)
25362, thanks. I only have water so.. :)

RE: Pressure rise in closed system.?

(OP)
A small follow up, If I was to determine how much the water will expand, how do I calculate this? Let’s say I have 20ccm3 @ 1atm and 20C. Now I add heat until it reaches 90C, how much has the water expanded?

RE: Pressure rise in closed system.?

Ferlev, if still in fixed 20 cc container, the water doesn't expand, only the pressure increases.

But expanding a constant weight of water (w/o any evaporation loss) at 1 bar, you can use the cubic thermal expansion expression given by 25362 or just look up the density of water in handbooks.  The CRC Handbook of Chemistry & Physics gives the following:
T, oC   Density, g/cc  Vapor Pressure, kPa
20        0.99821             2.3388
70        0.97778            31.176
90        0.96535            70.117

So, under 1 bar total pressure, 20 cc of water at 20oC would expand to (0.99821/0.96535)x 20 = 20.68 cc.

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