Pressure rise in closed system.? 2

[Ferlev]

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!

 

[sailoday28]

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

Regards

 

[Ferlev]

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.

 

[sailoday28]

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

 

[zdas04]

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

http://www.muleshoe-eng.com

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

The harder I work, the luckier I seem

 

[25362]

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 30^oC:

(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.

 

[Ferlev]

Thanks for the quick replys. This give me a fair view of the situation.

 

[25362]

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.

 

[Ferlev]

25362, thanks. I only have water so..

 

[Ferlev]

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?

 

[kenvlach]

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 20^oC would expand to (0.99821/0.96535)x 20 = 20.68 cc.