CALCULATION OF DENSITY, ENTHALPY AND ENTROPY FOR SUPERCRITICAL CARBON DIOXIDE
Here the thermodynamic properties for carbon dioxide are calculated from the Stryjek and Vera modification of the PengRobinson equation of state (PRSV)^{1}. This is not the most accurate equation of state for carbon dioxide, but it gives reasonable values. By entering the pressure and temperature into the calculation below, the density, enthalpy and entropy of carbon dioxide are displayed, The values for enthalpy and entropy given are relative to the values for carbon dioxide as an ideal gas at one atmosphere and 25°C. To convert to absolute values it is necessary to add 35616 J mol^{1}to the enthalpies and 213.7 J mol^{1} K^{1} to the entropy.
Pressure 
Bar 
Temperature 
K 


Density 

Enthalpy 

Entropy 

The
other functions of state can be calculated from the above, after defining some
quantities as follows.
p, pressure, in Pa = 10^{5}
times the value of pressure given above
T, temperature, in K = the
temperature given above
r, density, in kg m^{3} = the density
given above
H, enthalpy, in J mol^{1}
= enthalpy given above
S, entropy, in J mol^{1}
K^{1} = entropy given above
Then
V, molar volume, in m^{3}
mol^{1} = 0.04401/r
U, internal energy, in J mol^{1}
= H – PV
A, Helmoltz energy, in J mol^{1}
= U – TS
G, Gibbs energy, in J mol^{1}
= H – TS
The
calculator only applies above the critical temperature. We are able to carry out bespoke
calculations for many different systems, including different materials and phases, so please contact us if this is
required. However, the calculator here
is very useful as an initial guide, as illustrated by the examples below.
If CO_{2} is expanded from 300 bar, at 343K in
an extractor to 100 bar in a separator without heating, what will the
temperature of the expanded gas be?
Assuming
no heat exchange with the environment, the process is adiabatic and
isentropic. To determine the
temperature after expansion, we need to find the temperature at 100 bar which
has the same entropy as 300 bar at 343K.
From the calculator, the start conditions are:
Pressure: 300 bar
Temperature:
343 K
Density: 784
kg / m^{3}
Enthalpy: 8462 J / mol
Entropy:
64.3 J/mol/K
At
305.5K and 100 bar, the entropy is –64.4 J/mol/K, i.e. approximately the same
as before, so after expansion we will have:
Pressure: 100 bar
Temperature:
305.5 K
Density: 692
kg / m^{3}
Enthalpy: 9675 J / mol
Entropy:
64.4 J/mol/K
For the above expansion, how much heat per kg do we
need to put in to keep the temperature the same?
If
the temperature is the same at 343 K, but the pressure falls from 300 bar to
100 bar, the calculator will show that the enthalpy becomes –3226 J / mol, i.e.
increases by 6449 J / mol. The molar
mass of CO_{2} is 0.044 kg, so this equals 147 J / g, or kJ / kg.
If
we have a system operating at 1000 kg / hr (278 g/ s), this equals 278 x 147 = 40866
J / s (W). Therefore we will need 41 kW
of heating at this stage.
I seal a vessel containing CO_{2} at 305K and 100 bar, and heat it to
350K. What will the resulting pressure be?
Here,
the volume and weight of the gas if fixed, so the density is fixed. We need to find the pressure at 350K so that
the density is the same as at 305K, 100 bar.
The starting density is 699 kg / m^{3}. At 350 K the density is 698 kg / m^{3}
at 261 bar, so this is pressure that will be reached in the vessel after
heating.
I don’t have a pump, but want to achieve a pressure of
CO_{2} in a 100 mL sealed vessel by adding dry ice and heating to
323K. How much dry ice do I need?
Here,
we know the pressure and temperature, so using the calculator we find the
density is 378 kg / m^{3}, or 0.378 g/mL. The volume is 100 mL, so the weight of dry ice needed is 37.8g.
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A.A Clifford 04/12/2007