For example, a 500 ml reactor was filled with 250 ml water. The reactor was tightly sealed and heated until 200 C.
We know that not all of the water become steam because the vessel volume is not expanding. But, the density of the water is changing.
How to calculate the water expansion?
The Volumetric expansion DV is
dV = V1 - V0 = change in volume (m3, ft3)
The change in the units volume when temperature changes can be expressed as
dV = V0 β (t1 - t0)
β = volumetric temperature expansion coefficient(m3/m3 oC, ft3/ft3 oF)
t1 = final temperature (oC, oF)
t0 = initial temperature (oC, oF)
The density of a fluid when temperature changes can be expressed as
ρ1 = m / V0 (1 + β (t1 - t0))
= ρ0 / (1 + β (t1 - t0))
where
ρ1 = final density (kg/m3, lb/ft3)
ρ0 = initial density (kg/m3, lb/ft3)
If the initial temperature is 35 degree C then
Final Volume is 279 ml
The density of most liquids is almost independent of pressure. However, the pressure above the water has to be high enough at 200C to keep some of it in the liquid phase. The NIST web book has the ability to calculate accurate values for a lot of water's properties as a function of temperature and pressure. For example, to calculate the density of water at 200C one would need a minimum pressure in the flask of ~15.5 atm. (see https://webbook.nist.gov/cgi/fluid.cgi?T=200&PLow=1&PHigh=20&PInc=1&Applet=on&Digits=5&ID=C7732185&Action=Load&Type=IsoTherm&TUnit=C&PUnit=atm&DUnit=g%2Fml&HUnit=kJ%2Fmol&WUnit=m%2Fs&VisUnit=uPa*s&STUnit=N%2Fm&RefState=DEF )
At 200C the vapor pressure of water is ~16 atm, so liquid water can exist.
From the above NIST web page we find the density of water at 16 atm to be about 0.846 gm/ml.
The original 250 ml of water is approximately equal to 250 grams of water. Thus the volume occupied by the water at 200C would be approximately
250/0.864 ~= 289.5 ml.
One should check the head space to see how much water would have to evaporate to get the pressure up to 16 atm, but the estimate above should be reasonable.
The Volumetric expansion DV is
dV = V1 - V0 = change in volume (m3, ft3)
The change in the units volume when temperature changes can be expressed as
dV = V0 β (t1 - t0)
β = volumetric temperature expansion coefficient(m3/m3 oC, ft3/ft3 oF)
t1 = final temperature (oC, oF)
t0 = initial temperature (oC, oF)
The density of a fluid when temperature changes can be expressed as
ρ1 = m / V0 (1 + β (t1 - t0))
= ρ0 / (1 + β (t1 - t0))
where
ρ1 = final density (kg/m3, lb/ft3)
ρ0 = initial density (kg/m3, lb/ft3)
If the initial temperature is 35 degree C then
Final Volume is 279 ml
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