Enthalpy

1
Enthalpy

• important in flow systems where temperature and
  chemical composition play an important role
• h u Pv
• h specific enthalpy, (kJ/kg, J/mol, Btu/lb
  etc.)
• u specific internal energy
• P pressure
• v specific volume
• Units for u and Pv obviously need to be
  consistent with h

2
Specific enthalpy for a pure substance

• From phase rule, C1, P1, F2
• Thus, hh(T,P)
• For ideal gases hh(T)
• Holds for many other substances as well
• Notable exception STEAM
• (Thats why we need steam tables to look up
  properties of superheated steam and compressed
  liquid as a function of both T and P)

3
Change of enthalpy with temperature
4
Change of enthalpy with phase

• The (latent) heat of vaporization at T
• Heat of fusion at T
• Heat of sublimation at T

5
h vs T, including phase changes
6
Enthalpy of a mixture - ideal mixtures

• Simply add the enthalpy of the components to get
  the total enthalpy

7
Enthalpy of a mixture - nonideal mixtures11?2 !

• Examples strong acid and base solutions
• The resulting solution must have less energy than
  the sum of the energies of its constituents at
  the same temperature and pressure.

8
Absolute (relative ?) value of h choosing a DATUM

• We can calculate changes in specific enthalpy by
  dhCpdT
• What about the absolute value? hh(T)
• Remember h is what we need, to find Hmh

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Properties of humid airexpressed per unit mass
of BDA
10
Properties of humid airexpressed per unit mass
of BDA
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Temperatures and temperature differences

• Temperature
• Temperature difference
• ?C ?K
• ?F ?R
• ?F 1.8 ?C

12
Energy balancefor a flow system dominated by
thermal and composition effects

• Hin Q Hout W
• Where
• Hin, Hout The enthalpy of the material
  entering and leaving the system
•  
• Q heat (thermal energy) added to the system by
  heat transfer (conduction, convection,
  radiation)
• Q UA(Tsurroundings - Tsystem)
•  
• W Work done by the system on the surroundings
  (via some mechanical means like a shaft)
•  
• Each or these terms has units of energy, kJ, Btu,
  etc.

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Strategy for Analyzing Energy Balance problems

• See strategy for analyzing material balance
  problems.
• - Usually the material balances have to be solved
  first before the energy balance is attempted, so
  that the ms are known.
• - Sometimes they are simultaneous.
• - No problem that involves just an energy
  balance.
• Never start with the energy balance
• Choose a DATUM for all components going in and
  out of your system, so that the hs can be
  calculated.
• Determine the status of Q
• - Unknown the energy balance has to be solved
  for Q
• Known the energy balance can be used as one
  more equation to solve for an unknown (a material
  balance unknown, temperature, or state
• Often we are interested in the adiabatic, Q0,
  case

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• SYSTEM Wet Bulb
• Large amount of air blown over the wet bulb
  (temperature and humidity of the air in and out
  are the same)
• System is really not at steady state since the
  water on the wick is evaporating. However, the
  wet bulb temperature is established pretty
  quickly and is maintained until all the water is
  evaporated. So we can analyze the flows at steady
  state.
• MASS BALANCES
• air IN OUT
• water DEPLETION OUT

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Wet bulb

• ENERGY BALANCE Hin Q Hout
• Datum BDA _at_ Tair, H2O (liquid) _at_ Twb
• Hair Q Hair H evaporated water
• kg mass transfer coefficient, hc heat
  transfer coefficient

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Wet bulb energy balance
17

• SYSTEM Adiabatic saturation tower
• MASS BALANCES
• BDA 1 kg BDA in 1 kg BDA out (BASIS)
• Water w kg in with air m kg make-up ws kg
  out with air

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Adiabatic saturation

• ENERGY BALANCE Hin Hout
• Datum BDA _at_ Ts, H2O (liquid) _at_ Ts

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Adiabatic saturation energy balance
20

• Energy balance on wet bulb

• Energy balance for adiabatic saturation

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Energy balance for systems with chemical reaction

• So far we have considered the change of enthalpy
  only with temperature and phase (solid, liguid,
  vapour)
• Thus, in choosing a DATUM we have only specified
  a temperature and a state, e.g. H2O (liquid) at 0
  C, BDA at 0 C etc.
• What about the following system?

1 mol CH4 2 mol O2 At 25 C, 1 atm
1 mol CO2 2 mol H2O At 25 C, 1 atm
22
1 mol CH42 mol O2At 25 C, 1 atm
1 mol CO22 mol H2O (g)At 25 C, 1 atm
Q

• If we set DATUM 25 C for all gases
• Then, Hin Hout 0, and Q Hout Hin 0
• However, when we carry out this process, we
  observe that
• Q - 802.32 kJ, i.e. the system gives off
  energy to the surroundings
• It looks like there is generation of energy in
  the system.
• So we revise our energy balance to read
• Hin Q heat generated Hout

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• We know that energy is neither created nor
  destroyed but can change from one form to another
• So what we are observing in a chemical reaction
  is the transformation of energy from one form to
  another
• We are transforming the bond energies in the
  molecules to thermal energy
• We cannot measure bond energies by measuring the
  temperature or phase of a substance, so it
  appears as if energy is being created
• Other reactions may appear to consume energy.

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• The negative sign indicates an exothermic
  reaction,
• i.e. the reaction creates energy
• The opposite is an endothermic reaction,
  consuming energy
• We calculate ?H0rxn by
• Where the ?h0f are the standard heats of
  formation for each compound, tabulated in
  chemistry texts.
• The superscript 0 refers to the standard state
  (25 C, 1 atm)
• The bar over the H indicates that the value has
  been calculated
• for the indicated quantity of reactans/products,
  i.e. 1 mol of methane

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Energy balance with chemical reaction The Heat
of reaction approach

• We revise the energy balance to include a term to
  account for the heat effects of chemical
  reactions
• Hin Q heat generated Hout
• Using the convention for exothermic and
  endothermic reactions, we we can write this as
• When ?Hrxn is negative we end up with a positive
  value for heat generated, and vice versa
• The ?Hrxn term must account for the actual amount
  of reaction that took place.
• It must account for reactants going to products
  at the specified DATUM
• The DATUM does not have to be at 25 C but it is
  almost always more convenient to choose a DATUM
  of 25 C

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• The standard heats of formation are themselves
  the heats of reactions that form the compounds
  from the constituent elements in their stable
  forms at 25 C and 1 atm.
• e.g.
• The heat of formation of elemental species are 0!
  (by definition)

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Energy balance with chemical reaction The heat
of formation approach

• We retain the energy balance developed for
  non-reacting systems
• Hin Q Hout
• However, we recognize that the enthalpy of any
  material entering or leaving the system must
  account for differences in enthalpy due to the
  chemical bond structure of the material. We
  therefore add a term to the specific enthalpy of
  substances

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The heat of formation approachDATUM Elements
in their natural states at 25 C and 1 atm