1 reply to this topic

[August]

To calculate the volume of water after heated, can I simply use the density of water at different temperature?

 

I found a formula dV = V₀ β (t₁ - t₀) 

which gives different results from calculating by density. 

 

Also, the formula to calculate the density of water at different temperature ρ₁ = m / V₀ (1 + β (t₁ - t₀))

    = ρ₀ / (1 + β (t₁ - t₀))         giving different results from the experimental data.

 

[serra]

you can calculate the so called volumetric expansivity coefficient or (1/V)*dV/dT
if you have a table of values (volumes vs. temperature) you can for example do a numerical differentiation or (better) fit values with some function and differentiate function.
For accurate results you need a suitable model, as far as I know the most accurate is IAPWS 1995, this model allows to calculate volumes at different temperatures and evaluate differences.
A better option is to calculate directly the different derivatives of the model,
some software as the ASME Steam Tables or Prode Properties do that,
with Prode the macros
=strLVE(1) or =EstrLVE(1,t,p)
in Excel return directly volumetric expansivity coefficient

for example at 20 C 1 Bar.a value is 0.0002068 1/K
note the value is not constant vs. temperature

for example if you calculate the volume (M3) of 1 Kg of water with Prode and IAPWS 1995
at  20 C 1 Bar.a value is 0.00100179 M3

with this value and the volumetric expansivity coefficient you can estimate
the volume at 21 C 1 Bar.a
=0.00100179*(1+0.0002068*(21-20)) = 0.001002004 M3

now you can compare this estimated value with the volume calculated by model with macro =EstrV(1,21,1)
=0.001002009 M3 which is very close

however if you repeat the calc's at 30 C you obtain
=0.00100179*(1+0.0002068*(30-20)) = 0.001003868 M3

while the model returns 0.00100437

by the way you get similar errors on estimates of volumes or densities at different pressures from isothermal compressibility coefficient -(1/V) dV/dP

 

another possibility is to adopt average values for volumetric expansivity coefficient or isothermal compressibility coefficient over a range of values.