Calculation of Enthalpy Changes

1
Calculation of Enthalpy Changes

• How do we calculate enthalpy (and internal
  energy) changes when we dont have tabulated data
  (e.g., steam tables) for the process species?
• In this lecture we will examine ways to calculate
  enthalpy (and internal energy changes) associated
  with the following processes
• with change in P (at constant T and phase)
  (8.2 FR)
• with change in T (at constant P and phase)
  (8.3 FR)
• with change in phase (at constant T and P)
  (8.4 FR)
• To keep track of our calculations, we will
  summarize enthalpies in an Inlet-Outlet Enthalpy
  Table.

2
Hypothetical Process Paths

• To calculate enthalpy changes, we need to
  construct a hypothetical process path, where
  
• Starting point your defined reference state (T,
  P and phase)
• End point the conditions of the stream of
  interest (inlet or outlet)
• Since and are state properties (values
  are only dependent on the state of the species
  and not how they got there), any convenient
  process path from a reference state to a process
  state can be chosen
• The ideal process path will allow you to make
  use of
• sensible heats ? heat capacities
• phase transition temperatures ? Tm, Tb
• latent heats ? heat of vapourization, heat of
  melting

3
Hypothetical Process Paths

• Calculate the enthalpy change as 1 kg of ice at
  0?C is transformed to superheated steam at 400?C
  at 10 bar.
• We could use the steam tables and find
• How would we calculate the enthalpy change if we
  didnt have the steam tables?

4
Hypothetical Process Path
reference state
5
Changes in Enthalpy and Internal Energy with P

• Ideal Gases
• By definition, (molecules dont
  interact, so changing P doesnt change the
  internal energy)
• ?H ?U ?PV but ?PV ?nRT 0 (constant T) ?
• Non-Ideal Gases
• Changes in internal energy and enthalpy are
  small, provided ?P is small (lt 5 atm) ?
• For steam, use tabulated values
• Liquids and Solids
• (but still very small)

In a problem, state that changes in U and H are
small and will be neglected (except for steam
tables).
6
Phase Changes Latent Heat

• Phase changes occur from the solid to the liquid
  phase, and from the liquid to the gas phase, and
  the reverse. The specific enthalpy change (heat)
  associated with the phase change at constant T
  and P is known as the latent heat of the phase
  change (i.e., latent heat of vapourization or
  simply heat of vapourization).

Table B.1 reports these two latent heats for
substances at their normal melting and boiling
points (i.e., at a pressure of 1 atm).
7
Single Phase Heating Sensible Heat
Sensible heat refers to heat that must be
transferred to raise or lower the temperature of
a substance without change in phase.

• Sensible heat of solid, ?H (Tinitial
  ?Tmelting)
• Sensible heat of liquid, ?H (Tmelting ?
  Tvapourization)
• ? Sensible heat of liquid, ?H
  (Tvapourization ? Tfinal)

?Hvapourization
?
?Hmelting
?
?
Tinitial
Tfinal
8
Changes in Enthalpy and Internal Energy with T

• The quantity of sensible heat required to produce
  a temperature change in a system can be
  determined from the appropriate form of the first
  law of thermodynamics

Ideal gas exact Solid or liquid good
approximation Nonideal gas valid only if V
constant
Slope Cv heat capacity at constant volume
9
Changes in Enthalpy and Internal Energy with T

• Enthalpy, like internal energy, also depends
  strongly on temperature.

Ideal gas exact Solid or liquid good
approximation Nonideal gas exact only if P
constant
Cp heat capacity at constant pressure
Liquids and Solids Cp ? Cv
Ideal Gases Cp Cv R
10
Heat Capacity Formulas

• Heat capacity the amount of heat required to
  raise the temperature of one mole or one gram of
  a substance by one degree Celsius without change
  in phase
• units
• Heat capacities are functions of temperature and
  are expressed in polynomial form
• Cp a bT cT2 dT3
• or,
• Cp a bT cT-2
• Values of coefficients a, b, c, and d are given
  in Table B.2.

11
Notes Regarding Table B.2

• Be sure you use the correct functional form
• Cp a bT cT2 dT3 (Form 1) or Cp a
  bT cT-2 (Form 2)
• Temperature units are sometimes K and sometimes
  ?C
• Positive exponent in table heading means you use
  negative exponent in the expression
• E.g., if a x 103 123.0 ? a 123.0 x 10-3
• Be careful when you integrate! (T22 T12) ? (T2
  T1)2

12
Heat Capacity Calculations Integration
13
Specific Enthalpies of Gases Table B.8

• Table B.8 lists specific enthalpies of selected
  gases (mainly combustion products) as a function
  of temperature.
• The reference state of these gases is 1 atm and
  25?C
• Use this table like you would for the steam
  tables.
• Interpolation may be required.