ME481/581: Homework Two
Fall 2001
Prof. W. H.
Warnes
Office: Rogers Hall 308
Phone and Voice Mail: (541) 737-7016
FAX (541) 737-2600
DUE Friday, October 12, 2001
This page last updated October 13, 2001
email:
warnesw@engr.orst.edu
Enthalpy Calculations
1) Use the data from the CRC Handbook to calculate the ENTHALPY as a function
of temperature for pure Al in both the liquid and solid phases over a temperature
range of 700 K - 1200 K. Plot the two functions, and determine the latent
heat of fusion by calculating the difference in the enthalpies of the two
phases at the equilibrium melting temperature.
2) Using the equation for the enthalpy of mixing we derived in class, plot
the value of the mixing enthalpy as a function of composition. Assume that
you have one mole of a regular solid solution with a BCC crystal structure,
with e positive, and taking values of 5 kJ/mole, 50 kJ/mole, and 500 kJ/mole.
Gibbs Free Energy Calculations
3) Calculate the Gibbs free energy as a function of temperature for solid
Al over the temperature range of 700 K - 1200 K using BOTH the CRC Handbook
Data, and the CALPHAD data (for FCC Al). Plot both curves on the same plot
and describe how well they compare to one another. (NOTE: Remember to convert
to consistent units between the two graphs. I recommend using J/mole.)
Random Solutions
4) Assuming a random binary solution, plot the values of the fraction of
AA bonds (fAA), fBB, and fAB versus composition.
ME481 Extra Problems: (ME 481 students must do this in addition to the above
set).
None this week.
ME581 Extra Problems: (ME 581 students must do this in addition to the above
set).
5) Use the CALPHAD data for liquid and solid (FCC) Al to calculate the Gibbs
free energy and find the equilibrium melting temperature of Al.
SOLUTIONS
1) Use the data from the CRC Handbook to calculate the ENTHALPY
as a function of temperature for pure Al in both the liquid and solid phases
over a temperature range of 700 K - 1200 K. Plot the two functions, and determine
the latent heat of fusion by calculating the difference in the enthalpies
of the two phases at the equilibrium melting temperature.
From the preface page to the CRC Handbook data, we see that
equation 2 gives us the fitting function for the enthalpy as a function of
temperature:
I plugged the correct values into an EXCEL spreadsheet and found
the following plots:
My calculated values of the enthalpy at Tm = 933.2 K are H(solid
Al) = 1717.1 cal/g-mole, and H(liquid Al) = 6202.4 cal/g-mole, so that the
DELTA H = Latent Heat = 4.49 kcal/g-mole.
Just to put this in perspective, if you calculate the specific
heat of the solid Al at the melting point (again using the CRC data) and divide
that into the latent heat, you have an estimate of the temperature rise that
much energy would create if it were all dumped into the solid Al at one time
(the latent heat is released during the freezingof the liquid). The answer
is a whopping 585 K temperature rise! The message here is that the heats of
transition can be BIG, and also that we have to allow time to remove the heat
during the freezing process, which gets into solidification processes and
casting.
2) Using the equation for the enthalpy of mixing we derived in class, plot
the value of the mixing enthalpy as a function of composition. Assume that you
have one mole of a regular solid solution with a BCC crystal structure, with
e positive, and taking values of 5 kJ/mole, 50 kJ/mole, and 500 kJ/mole.
The BCC structure tells us that the number of nearest neighbors, z = 8. Now
we plug and chug and plot:
3) By my calculations, the two results come out pretty much the same...
4) Assuming a random binary solution, plot the values of the fraction of
AA bonds (fAA), fBB, and fAB versus composition. The equations from class
used to calculate the fraction of each bond type are:
ME481 Extra Problem: (ME 481 students must do this in addition
to the above set).
None this week.
ME581 Extra Problem: (ME 581 students must do this in addition
to the above set).
5) Use the CALPHAD data for liquid and solid (FCC) Al to calculate
the Gibbs free energy and find the equilibrium melting temperature of Al.
I found the temperature at which they are equal is between 930 and 940 K on
my plot, good agreement with the listed value of 933.6 K.
End of File.