Material and Energy Balances
An EXCEL Spreadsheet for Computing Enthalpy Changes and
Mean Specific Heat Capacities for Ideal Gas Mixtures
Brice Carnahan – University of Michigan
Introduction
For ideal gas mixtures, H, the change in enthalpy between an initial and final state or the enthalpy
difference between the inlet and outlet streams in a flow process without reaction or phase changes (e.g.,
in a heat exchanger), is:
1) a function of temperature T only,
2) the sum of the enthalpy changes for the individual mixture constituents, treated as pure
ideal gases.
For the ith constituent gas, the specific enthalpy change Hi (equation 8.3-10b in Felder) and mean
molar heat capacity Cpi (equation 8.3-15) are given by:
T2
Hi =
  Cpi(T) dT
T1
Cpi = HiT
(1,2)
The total enthalpy change H and mean heat capacity Cp for a mixture containing ni moles of the ith
constituent (i=1,...,N) is given by:
N
H = ni Hi
i=1
Cp = H/( M T)
(3,4)
Here, M is the total number of moles in the gas mixture, n1 + n2 + ... + nN; N is the number of
constituents.
Problem Statement
Prepare a general-purpose EXCEL spreadsheet that:
(1) Contains bordered cells where the user will enter values for:
a) The initial and final temperatures, T1 and T2 (deg C)
b) The mass (rate) in gmol of each of the N constituents, ni, i=1,...,N.
(2) Contains values for the constants a, b, c, and d for the type 1 polynomial approximations, C pi(T),
listed in Table B.2 (p 635 of Felder) for the following gases: acetylene, air, ammonia, carbon dioxide,
carbon monoxide, ethane, ethylene, helium, hydrogen, methane, methanol, nitric oxide, nitrogen, nitrogen
dioxide, nitrous oxide, oxygen, propane, propylene, and water.
(3) Evaluates the pure gas specific (molar) enthalpy change (eqn. 1) and mean molar heat capacity
(eqn. 2) for each constituent present in the mixture. These values should be computed by integrating the
polynomial approximation for the appropriate Cpi(T).
(4) Determines the total enthalpy change (eqn. 3), the specific molar enthalpy change H/M), and
the mean molar heat capacity (eqn. 4) for the mixture.
(5) Displays a linked bar chart showing the mole fraction of each constituent in the gas.
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Organize your spreadsheet as you like, clearly labeling and outlining the cells to be filled in with data
(use the bordering feature of the Cell entry of the Format menu). Gridlines and the row and column
labels and gridlines can be removed from the printed spreadsheet by checking appropriate entries in the
View tab of the Preferences entry of the File Menu. The reduce and page orientation (Page Setup in the
File menu) features for laser printing can be used to fit the entire sheet onto one printed page if the
spreadsheet is too big otherwise.
Test Cases
You should test your spreadsheet carefully to insure that it can handle general mixtures of the given
compounds. Once you have done that, use your spreadsheet to analyze the following mixtures:
1. 0.1 gmol each of Air, O2, N2, H 2, CO, CO2, and H2O with T1 = 25 oC and T2 = 1000 .oC Note
that your results for the pure component mean molar heat capacities should agree with the entries for
1000 oC in Table 8.3.1 in FR (the tabulated values in this table are for a reference temperature of 25 oC).
2. 0.1 gmol each of Air, O2, N2, H 2, CO, CO2, and H2O with T1 = 24.9 oC and T2 = 25.1. oC.
Note that your results for the pure component mean molar heat capacities should agree with the entries
for 25 oC in Table 8.3.1 in FR (the tabulated values in this table are for a reference temperature of 25 oC,
so the entries for 25 oC are the actual as well as mean heat capacities at 25 oC. Your spreadsheet can
similarly be used to calculate the actual heat capacity Cpi(T) for any of the components at any
temperature T; just enter two temperatures T 1 and T2 that are very close to the desired temperature T
(T1 and T2 must not be identical, however).
3. 90 gmol of C2H6 and 60 gmol of C3H8 with T1 = 0 oC and T2 = 400 oC (see Example 8.3-4 in
FR).
4. 60 gmol CH4 and 40 gmol H2O with T1 = 350 oC and T2 = 120 oC (see p 355 in FR).
5. 8.93 gmol CH4 and 80.37 gmol Air with T1 = 20 oC and T2 =300 oC (see Example 8.3.5 in FR).
6. 0.5 moles of each of the spreadsheet gases with T 1 = 250 oC and T2 = 750 oC.
7. Problem 8.16 in FR.
8. Problem 8.23 in FR.
9. Use the "Goal seek" feature of Excel (Formula menu) for the mixture of problem 6 with T 1 = 250
oC. Initially set T to 750 oF. In this case, find the final temperature T that will produce a total enthalpy
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change of 400,000 J.
10. Use the "Goal seek" feature of Excel for the mixture of problem 6 with T 1 = 250 oC. Initially, set
T2 to 750 oC. In this case, find the final temperature T2 that will produce a mean molar heat capacity of
45 J/gmol.
What to Turn In
1. A printed spreadsheet for each of the 10 problems assigned above. Print each spreadsheet on a
single page.
2. One printed spreadsheet showing the cell formulas (click on the "Formulas" button in the View tab
of the Preferences entry of the File menu to see the formulas). If a cell formula cannot be seen
completely (because of limited cell space), widen the columns before printing so that the complete
formula in every cell on the spreadsheet will show up. For this case, the printout may require more than
one page.
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BC
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