Lecture 2 Thermochemistry
Design a power plant X.S. Bai Thermochemistry
When we study a combustion device, what do we want to know? heat generated power production combustion efficiency combustion control Temperature pressure species concentrations flow velocity
When we study a combustion device, what do we want to know? X.S. Bai heat generated power production combustion efficiency combustion control Temperature pressure species concentrations flow velocity Thermochemistry
Outlines Multi-component mixture definition of thermodynamic variables Law of mass conservation molecules are not conserved elements are conserved First Law of thermodynamics energy is conserved Second Law of thermodynamics chemical reactions follows certain directions
Mixture in a combustion system
Mixture of a combustion gas (1) Mixture of a combustion gases contains fuel (contain C, H, O ) fossil fuels (Coal, natural gas, gasoline, kerosene..) biomass fuel (wood chips, city waste ) air (23.3% oxygen, 76.7% nitrogen in mass) Products CO 2 (green house gas) H 2 O minor species (CO, soot, NOx )
Mixture of combustion gas A macro-scopic view
Mixture of combustion gas (2) A micro-scopic view Molecules in a gas mixture moves randomly at a speed of sound, the distance between molecules is in the order of mean free path Time 1 Time 2 Time 3
Molecule Units A molecule consists of atom. An atom consists of nucleus and electrons. A nucleus consists of protons and neutrons... 1 proton weighs 1.6726 x 10-27 kg 1 neutron weighs about the same as 1 proton 1 electron weighs 0.9109 x 10-30 kg Too light? 1 mole molecules = 6.0221 x 10 23 molecules 1 mole C weighs = 12 g molecular weight [kg/kmole]
Mixture (3) In a combustion system, usually there are a lot of species (different molecules), say N. It is often useful to know mass percentage and mole percentage mass fraction Y i = mole fraction X i = number of mole i = mass of species i total mass number of moles of i total number of moles mass of species i molecule weight of i Species i = all molecules of type i Ex: 1 kg CO = 1000/28=36 mole CO
Mixture (4) Mole concentration, mole fraction and mass fraction can be converted if the molecule weight of species is known. Y i = X i MW i MW mix, X i = Y i MM mix MW i, C i =! Y i MW i N MW mix = " X i MW i = i=1 # % $ N " Y i MW i i=1 & ( ' )1
Mixture (5) The concept of stoichiometry stoichiometric air-fuel ratio (A/F) stoic =(m air /m fuel ) stoic stoichiometric fuel-air ratio (F/A) stoic =1/(A/F) stoic For a stoichiometric methane/air and propane/air system calculate the above quantities equivalence ratio φ=(a/f) stoic / (A/F)=(F/A)/(F/A) stoic percent stoichiometric air =100%/φ methane 17.16 1 Propane 15.60 1 A/F φ percent excess air = 100%*(1- φ)/φ
Mixture (6) - ideal gas The concept of ideal gas An ideal gas is referred to a gas that has no inter-molecular forces and no volume introduced in relating pressure and density (equation of state) p /! = nr u T, n = N Y i " = i=1 MW i 1 MW mix p i = X i p = X i MW mix!r u T
Mixture of combustion gas (7) - macroscopic view 1 m 3 air at standard condition contains about 30 mole molecules, that is 1.8*10 25 molecules. Tennekes & Lumley (A first course in turbulence) The smallest flow scale is Kolmogrov scale η 10 4 m the distance between molecules is the mean free path ξ 10 8 m the ratio between these scale is 4 ξ / η 10 Ma / Re So, it can be assumed that in combustion system, the gases can be treated as continuum media. 1/ 4
Mass conservation in a combustion system
Law of mass conservation In the universe, matters can be transformed to different forms, but the total mass of the matter involved in the transformation is not changed
Mass conservation in a combustion system Matter is comprised of molecules; molecule is comprised of atoms; atom is comprised of nuclei and electrons, nucleus is comprised of protons and neutrons H H H2 o : o
Mass conservation in a combustion system Processes involving formation and destruction of new molecules are referred to as chemical reactions Combustion involves only chemical reactions molecules are not conserved in combustion atoms (elements) are conserved in combustion!!!
Mass conservation in a combustion system A chemical reaction can be denoted as ex. CO+0.5O 2 CO2 this equation indicates 1 mole of CO react with 1/2 mole of oxygen and form 1 mole of carbon dioxide recall 1 mole of matter = 6.02*10 23 molecules In the above example none of the three molecules are conserved, but the two atoms involved (C & O) are conserved. The factor 0.5 is due to C & O conservation during chemical reactions In general N i= 1 ' i ν M i N i= 1 '' i ν M i
Mass conservation in a combustion system How to use Law of mass conservation to compute Y i use mass conservation of N atoms to construct N algebraic equations For a C, H, O, N system, 4 algebraic relations are obtained Y J m J = mj = i MW MW J i Y i n Ji Number of atom J in molecule i
Mass conservation example: biomass combustion 10 kg of dry wood chips are supplied to a combustor C (52% mass) Air H (6% mass) O (41% mass) Products CO 2, H 2 O Find out: Stoichiometric Air CO 2, H 2 O
Mass conservation example biomass combustion Air required: x kg Total reactants: 10+x kg Total products: 10+x kg The final products are: CO 2, H 2 O, N 2 Conservation of C, H, N, O: 4 equations 4 unknowns: x, Y CO2, Y H2O, Y N2
Mass conservation example biomass combustion Air required: 62.52 kg Products YCO 2 =0.26291 YH 2 O=0.07446 YN2=0.66123
Energy conservation in a combustion system
Energy conservation in a combustion system First Law of thermodynamics says for a fixed mass system Energy can be converted from one form to another change of total energy = heat added to the system - work done by the system to the surroundings
Energy conservation in a combustion system Internal energy a sum of all the microscopic form of energy, which are related to molecular structure and degree of the molecular activity. Thermal energy and chemical energy has to be taken into account Kinetic energy Macroscopic form of energy related to the fluid motion Potential energy Macroscopic form of energy related to the fluid height
Energy conservation in a combustion system Kinetic energy Potential energy Energy transfer heat transfer work
Energy conservation in a combustion system Internal energy a sum of all the microscopic form of energy, which are related to molecular structure and degree of the molecular activity. Some physical insight to internal energy thermal energy sensible energy latent energy chemical energy nuclear energy
Energy conservation in a combustion system Some physical insight to sensible energy thermal energy sensible energy latent energy
Chemical bonds Water molecule Oxygen molecule Nitrogen molecule
Electron configuration of Neon
Chemical bonds
Energy in combustion systems Total energy of system per unit mass =e + 1/2v 2 + gz e=specific internal energy 1/2v 2 =specific kinetic energy, v=velocity gz=specific potential energy
Energy in combustion systems Energy conservation Change of total energy = heat to the system work done by the system to the surroundings!(e + 1 2 v2 + gz) =!Q " pdv for an adiabatic constant pressure system energy conservation says e + p /!+ 1 2 v2 + gz = const. Specific enthalpy: h=e+p/ρ
Energy conservation in a combustion system The concept of enthalpy has no direct physical meaning, just a combined property very useful in combustion system Zero enthalpy Enthalpy of the element in their naturally occurring state and at standard condition is zero
Energy conservation in a combustion system In combustion problems we assume gas mixtures are ideal N h =! h i Y i, e =! e i Y i, p =! p i, p i = X i p i=1 T! N i=1 h i = h 0 i,f + c pi dt T ref N i=1 The concept of enthalpy of formation: h i,f 0 to take into account the chemical energy, define a reference state (p=1atm, T=25C) and let enthalpy of formation for the element in their naturally occurring state zero. NASA has a dada base for most elements and compounds
Energy conservation in a combustion system The concept of zero enthalpy enthalpy is a relative quantity in isothermal flows in combustion, one must take into account the chemical energy in enthalpy!! And nuclear energy is not taken into account!! Zero enthalpy: element at its naturally existing state at standard condition has zero enthalpy
Energy conservation in a combustion system The concept of enthalpy of combustion (heat of combustion)
Energy conservation in a combustion system Using the concept of enthalpy to calculate adiabatic flame temperature (constant pressure system)
The second Law of thermodynamics The second law of thermodynamics: consider a fixed-volume, adiabatic reaction vessel (a close system), the system develops towards a state at which entropy reaches its maximum (or equivalently Gibbs free energy reaches its minimum). This state is a chemical equilibrium state It is an ideal state It is a important reference state
Chemical equilibrium Second Law of Thermodynamics CO+0.5O 2 CO 2 CO 2 CO+O 2? ds>0 ds<0 CO + H 2 O =CO 2 +H 2
Calculation of equilibrium quantities Element mass conservation First Law of Thermodynamics or equivalently given temperature Second Law of Thermodynamics specify a chemical equilibrium reaction Maximal entropy or minimal Gibbs free energy NASA code CEC86 available upon request
Summary Combustion is a process in which fuel oxidizes chemical energy is released in the form of sensible (thermal) energy, by breaking old bonds and forming new bonds First Law of thermodynamics deals with how the energy is converted Second Law of thermodynamics tells us the maximal extend of this conversion To know exactly how much energy is converted one needs to learn the next chapter - chemical kinetics