thermodynamics & stoichiometry...
TRANSCRIPT
Thermodynamics
• Thermodynamics is the study of the effects of work, heat, and energy on a system
• Thermodynamics is only concerned with macroscopic (large-scale) changes and observations
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Getting Started
• All of thermodynamics can be expressed in terms of four quantities
– Temperature (T)
– Internal Energy (U)
– Entropy (S)
– Heat (Q)
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The first law
• The first law of thermodynamics is an extension of the law of conservation of energy
• •The change in internal energy of a system is equal to the heat added to the system minus the work done by the system
– ΔU = Q -W
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Process Terminology
• Adiabatic –no heat transferred
• Isothermal –constant temperature
• Isobaric –constant pressure
• Isochoric –constant volume
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Thermodynamic system and control volume
• We take the following definitions:
– Thermodynamic system: an object and quantity under investigation,
– Surroundings: everything external to the system,
– System boundary: interface separating system and surroundings, and
– Universe: combination of system and surroundings
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Thermal equations of state
• Thermal equation of state: an equation which gives the pressure as a function of two independent state variables. An example is the general form:
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Material Balances on Reactive Processes
• Material balances on processes involving chemical reactions may be solved by applying:
– Molecular Species Balance – a material balance equation is applied to each chemical compound appearing in the process.
– Atomic Species Balance – the balance is applied to each element appearing in the process.
– Extent of Reaction – expressions for each reactive species is written involving the extent of reaction.
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Chemical Reactions, Atoms and Molecules in Combustion
• A chemical reaction is an exchange and/or rearrangement of atoms between colliding molecules, for example:
• The atoms are conserved (they are not created or destroyed) while molecules are not conserved.
• In the above reaction H, O atoms are conserved while molecules H2, O2 and H2O are not.
• Reactant molecules (H2 and O2) are rearranged to become product (H2O) molecules. Heat is released in this process.
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Amount of Substances, Mole and Mass Fractions
• Atoms and molecules are counted in amount of substances or moles. 6.023 · 1023 particles (atoms, molecules) are called one mole of the substance (Avogadro constant).
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• For a mixture of species:
– where n stands for total number of moles, ni is the number
of moles of species i, and the summation extends over all the species.
• Mole fraction –yi – (mole number) of species i is:
𝑦𝑖 =𝑛𝑖𝑛
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• The molar mass (molecular weight) in g/mol or kg/kmol is the mass of one mole of the species (for example: MC = 12 g/mol, MCO2
= 44 g/mol).
• The mean molar mass (molecular weight) of a mixture is:
𝑀𝑚𝑒𝑎𝑛 = 𝑦𝑖𝑀𝑖𝑖
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Molecular and Elemental Balances
• For steady-state reactive processes: Input + Generation = Output + Consumption
• The generation and consumption terms in the
molecular balance equation is usually obtained from chemical stoichiometry.
• But for an atomic balance, for all cases
Input = Output
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Dehydrogenation of Ethane
• Consider the dehydrogenation of ethane in a steady-state continuous reactor,
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• Total Balance: Input = Output
• Molecular Species Balance: – C2H6: Input – Consumed = Output
– C2H4: Generated = Output
– H2: Generated = Output
• Atomic (Elemental) Species Balance: – C-Balance: Input = Output
– H-Balance: Input = Output
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Independent reactions in gasification?
• C + O2 = CO2
• C + CO2 = 2 CO
• C + H2O = CO2 + H2
• CO + H2O = CO2 + H2
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Degrees of Freedom of Analysis for Reactive Processes
• Molecular Species Balance
+ No. identified/labeled unknowns
+ No. independent chemical reactions
– No. of independent molecular species
– No. other equations relating unknown variables
------------------------------------------------------------------
= No. degrees of freedom
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• Atomic Species Balance
+ No. identified/labeled unknowns
– No. independent atomic species
– No. of independent nonreactive molecular species
– No. other equations relating unknown variables
------------------------------------------------------------------
= No. degrees of freedom
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Independent Chemical Reactions, Molecular and Atomic Species
• Chemical reaction: A chemical reaction is independent if it cannot be obtained algebraically from other chemical reactions involved in the same process.
• Molecular Species: If two molecular species are in the same ratio to each other wherever they appear in a process, then these molecular species are not independent.
• Atomic Species: If two atomic species occur in the same ratio wherever they appear in a process, balances on those species will not be independent equations.
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Independent Chemical Reactions, Molecular and Atomic Species
• Consider the following reactions:
A =======> 2B
B =======> C
A =======> 2C
• Are these chemical reactions independent?
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Independent Chemical Reactions, Molecular and Atomic Species
• Consider a continuous process in which a stream of liquid carbon tetrachloride (CCl4) is vaporized into a stream of air.
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• Molecular Species Analysis
– Total: 3 (O2, N2, CCl4)
– Independent: 2 (O2 or N2, CCl4)
• Atomic Species Analysis
– Total: 4 (O, N, C, Cl)
– Independent 2 (O or N, Cl or C)
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Example. Production of Chlorine
• In a process for the manufacture of chlorine, HCl and O2 react to form Cl2 and H2O.
• Sufficient air (21 mole% O2, 79% N2) is fed to provide 35% excess oxygen and the fractional conversion of HCl is 85%.
• Determine the amount of air required per mole of HCl fed into the process.
• Calculate the mole fractions of the product stream components using: a. molecular species balances b. atomic species balances c. extent of reaction
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• Identify the components of the product stream:
– HCl since not all will be converted (based on fractional conversion)
– O2 since it is supplied in excess
– N2 it goes with the O2 in air but not consumed during the reaction
– Cl2 produced during the process
– H2O produced during the process
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• To get mole fractions of components in the product stream: yi = ni/nt
• For the identified components: yHCl = n2/nt
yO2 = n3/nt
yN2 = n4/nt
yCl2 = n5/nt
yH2O = n6/nt
where nt = n2 + n3 + n4 + n5 + n6
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• HCl Balance: Input – Consumed – Output = 0
(100 mol) – 0.85(100 mol) – n2 = 0
n2 = 15 mol HCl
• O2 Balance: Input – Consumed – Output = 0
(33.75 mol) – 85 mol HCl react (0.5/2) – n3 = 0
n3 = 12.5 mol O2
• N2 Balance: Output = Input
n4 = 160.7 mol air (0.79 mol N2/1 mol air)
n4 = 127 mol N2
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• Cl2 Balance: Generated – Output = 0
85 mol HCl react (1/2) – n5 = 0
n5 = 42.5 mol Cl2
• H2O Balance: Generated – Output = 0
85 mol HCl react (1/2) – n6 = 0
n6 = 42.5 mol H2O
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• From % excess O2 ======> n1
• From fractional conversion ======> n2
• Atomic Species Balance:
H-Balance: 100(1) = n2 + 2n6
O-Balance: n1(0.21)(2) = 2n3 + n6
Cl-Balance: 100(1) = n2 + 2n5
N-Balance: n1(0.79)(2) = 2n4
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