Here the thermodynamic properties for carbon dioxide are calculated from the Stryjek and Vera modification of the Peng-Robinson 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 | 0.0 KG/M^{3} |

Enthalpy | 0.0 J/MOL |

Entropy | 0.0 J/MOL/K |

^{1 }R. Stryjek, J. H. Vera, *PRSV: An Improved Peng –Robinson Equation of State for Pure Compounds and Mixtures*. The Canadian Journal of Chemical Engineering, **64**, April 1986

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*

## EXAMPLES

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.

# How big a heater do I need for the above expansion running at 1000 kg / hr?

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.