| Engineering Software is pleased to announce
the introduction of
Free Coursework
Material.
Engineering Software Coursework Material covers the following area:
Single Species Approach Introduction This section provides a Physical Properties analysis for single species. Analysis In the presented Physical Properties analysis, only ten (10) basic species are considered behaving as an ideal gas -- ideal gas state equation is valid -- pv = RT. For each reaction species, the thermodynamic functions specific heat, enthalpy and entropy as functions of temperature are given in the form of least squares coefficients as follows: Cp/R = A1 + A2T + A3T2 + A4T3 + A5T4 H/(R*T) = A1 + A2T/2 + A3T2/3 + A4T3/4 + A5T4/5 + A6/T S/R = A1lnT + A2T + A3T2/2 + A4T3/3 + A5T4/4 + A7 or S/R = A1lnT + A2T + A3T2/2 + A4T3/3 + A5T4/4 + A7 - lnp For each species, two sets of coefficients are included for two adjacent temperature intervals, 273 to 1,000 [K] and 1,000 to 5,000 [K]. The data have been constrained to be equal at 1,000 [K]. For example, physical properties for both reactants and combustion products are very important and need to be known in order to carry out successful combustion calculations. The plot in Figure 1 depicts how the species enthalpy values change with the temperature. The physical properties provided in this plot come from the JANAF Thermochemical Data - Tables, 1970.
Figure 1 -- Enthalpy vs Temperature In general, enthapy values increase with an increase in temperature. It is interesting to note that the enthalpy value for basic combustion elements such as carbon (C), hydrogen (H2), sulfur (S), oxygen (O2) and nitrogen (N2) is equal to zero at the standard combustion conditions of 298 [K] and 1 [atm]. Also, it should be mentioned that for ideal gas species, the enthalpy value is only dependent on the temperature. Assumptions Considered species behave as an ideal gas. Governing Equations For each reaction species, the thermodynamic functions specific heat, enthalpy and entropy as functions of temperature are given in the form of least squares coefficients as follows: Cp/R = A1 + A2T + A3T2 + A4T3 + A5T4 H/(R*T) = A1 + A2T/2 + A3T2/3 + A4T3/4 + A5T4/5 + A6/T S/R = A1lnT + A2T + A3T2/2 + A4T3/3 + A5T4/4 + A7 or S/R = A1lnT + A2T + A3T2/2 + A4T3/3 + A5T4/4 + A7 - lnp For each species, two sets of coefficients are included for two adjecent temperature intervals, 273 to 1,000 [K] and 1,000 to 5,000 [K]. The data have been constrained to be equal at 1,000 [K]. Also, U = H - p*v*MW or U = H - R*T G = H - S*T and u = h - p*v or u = h - R*T/MW g = h - s*T Legend: Cp -- Specific Heat [kJ/kmol*K] cp -- Specific Heat [kJ/kg*K] MW -- Molecular Weight [kg/kmol] R -- Universal Gas Constant [kJ/kmol*K] Gas Constant = R/MW [kJ/kg*K] H -- Enthalpy [kJ/kmol] h -- Enthalpy [kJ/kg] T -- Temperature [K] S -- Entropy [kJ/kmol*K] s -- Entropy [kJ/kg*K] p -- Pressure [atm] U -- Internal Energy [kJ/kmol] u -- Internal Energy [kJ/kg] v -- Specific Volume [m3/kg] G -- Gibbs Free Energy [kJ/kmol] g -- Gibbs Free Energy [kJ/kg] Input Data Table 1 - Enthalpy Values for Considered Species
at
Results
Figures
Conclusions In general, enthalpy values increase with an increase in temperature. It is interesting to note that the enthalpy value for basic combustion elements such as carbon (C), hydrogen (H2), sulfur (S), oxygen (O2) and nitrogen (N2) is equal to zero at the standard combustion conditions of 298 [K] and 1 [atm]. Also, it should be mentioned that for ideal gas species, the enthalpy value is only dependent on the temperature. References JANAF Thermochemical Data - Tables, 1970 |
Physical
Properties