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CBE2124, Levicky
1
Chapter 8 and 9 – Energy Balances
Reference States
. Recall that enthalpy and internal energy are always defined
relative to a reference state (Chapter 7). When solving energy balance problems, it
is therefore necessary to define a reference state for each chemical species in the
energy balance (the reference state may be predefined if a tabulated set of data is
used such as the steam tables).
Example
. Suppose water vapor at 300
o
C and 5 bar is chosen as a reference state at
which
H
ˆ
is defined to be zero. Relative to this state, what is the specific enthalpy of
liquid water at 75
o
C and 1 bar? What is the specific internal energy of liquid water
at 75
o
C and 1 bar?
(Use Table B. 7).
Calculating changes in enthalpy and internal energy
.
H
ˆ
and
U
ˆ
are
state
functions
, meaning that their values only depend on the state of the system, and
not on the path taken to arrive at that state.
IMPORTANT
: Given a state
A
(as characterized by a set of variables such as
pressure, temperature, composition) and a state
B
, the change in enthalpy of the
system as it passes from
A
to
B
can be calculated along any path that leads from
A
to
B
, whether or not the path is the one actually followed.
Example
. 18 g of liquid water freezes to 18 g of ice while the temperature is held
constant at 0
o
C and the pressure is held constant at 1 atm. The enthalpy change for
the process is measured to be
Δ
H
ˆ
=  6.01 kJ.
What would the
Δ
H
ˆ
for the process be if, instead, the 18 g of water is first heated
from 0
o
C to 100
o
C and entirely vaporized to steam at 100
o
C and 1 atm, then
liquified by compression from 1 atm to 10 atm at 100
o
C, than cooled to  200
o
C
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View Full DocumentCBE2124, Levicky
2
(during which step it freezes to ice) while being decompressed to a pressure of 1
atm, and finally thus formed 18 g of ice is heated from 200
o
C and 1 atm to ice at
0
o
C and 1 atm?
Types of Paths
. There are five types of paths for which we will learn to calculate
enthalpy changes
Δ
H
ˆ
:
1). Changes in pressure (
p
) at constant temperature (
T
) and state of aggregation
(i.e. no phase changes).
2). Changes in
T
at constant
p
and state of aggregation.
3).
Phase
changes
(i.e.
melting,
condensation,
evaporation,
solidification,
sublimation) at constant
T
and
p
.
4). Mixing steps (two liquids, gas in a liquid, solid in a liquid) at constant
T
and
p
.
5). Chemical reactions taking place at constant
T
and
p
.
The overall path from a state
A
to a state
B
will be able to be expressed as a
combination of the above five types of steps. Because enthalpy is a state function,
the total change
Δ
H
ˆ
for passing from state
A
to state
B
can be calculated as the sum
of the enthalpy changes
Δ
H
ˆ
j
for the individual steps,
Δ
H
ˆ
=
Δ
H
ˆ
1
+
Δ
H
ˆ
2
+
Δ
H
ˆ
3
+
Δ
H
ˆ
4
…
j
= 1, 2, …
k
(1)
where
k
is the total number of steps used, for purposes of the calculation, to take
the system from the initial state
A
to the final state
B
. Note that the steps used for
the calculation do not need to correspond to the actual path taken by the system
from
A
to
B
.
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 Fall '11
 Levicky

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