In this example we are looking at using heat of mixing information because we are going
to mix a pound of 20% sulfuric acid with a half a pound of 80% sulfuric acid.
They are both at 60 degrees and the question is how much heat do we need to remove from
this system so that the final mixture is also at 60 degrees Fahrenheit.
The process we are looking as is we have some mixer where we have 1 pound at 60 degrees
and it is 20% sulfuric acid.
Then we have a 1/2 pound also at 60 degrees and it is 80% sulfuric acid.
It means we have 1.5 pound, we want it to be at 60 degrees which means we may have to
add or remove heat.
We need to calculate what is the composition.
This is a weight percent.
That means the first thing we want to do is a mass balance on the process.
We will do a mass balance on sulfuric acid.
We have 1 pound and it is 20% sulfuric acid so that is 2 tenths a pound of sulfuric acid.
The 1/2 pound is 80% and that means we have 1.5 pounds with the percent a fraction of
"x" that we want to determine.
Not "x" percent here but let's call "x" the fraction.
We can solve for "x" as 0.40.
That means it is 40 weight percent in the exit.
In order to determine how much heat is added or removed we have to do an energy balance
and we have to have data.
I am going to use an enthalpy vs. weight percent sulfuric acid diagram from Smith and Vanessa.
I am going to read off the enthalpy for 20 percent solution -40 Btu/lb.
Then H2 is 80% so -118 Btu/lb.
H3, the exit, is -98 Btu/lb.
I am going to call this H1, this H2 and then the exit H3.
The energy balance is just delta H total equals Q. I am writing total here because in this
case H is not a specific enthalpy but it is a total enthalpy for the process.
Delta H is a final minus initial.
Final is 1.5 lb, enthalpy is H3.
Initial we had 1 lb with H1 and we also added 1/2 pound with H2.
This is all going to be equal to Q where the Q we calculate would be for 1.5 lbs leaving.
We have the enthalpy values for the table that we can substitute in here.
1.5 times -98 minus 1 times -40 and then minus 1/2 times -118 equals Q and this is BTUs that
we will ned up calculating.
Q is equal to -48 BTUs.
This says that the overall process is exothermic of mixing 2 sulfuric acid solution and we
have to remove heat to keep this isothermal so that the exit is at 60 degrees also.