Here we are going to do an energy balance
on a constant pressure process using the steam
tables.
We start with a liquid/vapor mixture and then
we're going to add heat.
We're going to do this at constant pressure.
And the question is what's the final temperature
and what phases are present.
First thing we want to do is draw a diagram
representing the process we're looking at.
So I've represented it as a piston so we add
more heat we expect to have more vapor, the
question is, Do we still have liquid remaining
in the system?
So we're going to do an energy balance.
We're doing an energy balance on a closed
system so the change of energy within that
system is Q plus W. So we're adding heat and
we know the work is at constant pressure.
Pressure, 450kPa, so minus P delta V which
means I can write this a delta PV.
And the reason I want to do that is so that
then I can rearrange this, take delta U, delta
PV is equal to the heat added.
Delta H, which is equal to H is U plus PV,
so the left is delta H, and the right then
is 2000 kJ.
So I need to now find the initial and final
values for the enthalpy and I use the steam
tables to do that.
So initially, I've called this state one,
there's a mixture of liquid and vapor so I'm
going to take the quality times the enthalpy
of vapor plus one minus the quality times
the enthalpy of the liquid.
That would give me the enthalpy per kg.
The problem says we have one tenth of a kg
of vapor and then the enthalpy of the vapor
I'm going to look up in the saturation tables
at 450 kPa, and this is 2743.1 this is kJ
per kg.
And then I have nine tenths of a kg of liquid
and it's enthalpy, again kJ per kg.
So H1, if I do this multiplication, 834.5
kJ.
H2 is just H1 plus our value Q.
So H2 is 2834.5 kJ.
And we're doing this calculation for one kg.
So the first thing we can notice is H2 is
larger than the enthalpy of saturated vapor
at this pressure.
Which means we must have superheated steam
and we would go to the superheated table,
for this case and the table that I'm using
we would have to interpolate.
So I'm going to write down the values for
the temperatures and show the interpolation.
So here from the steam tables, all at 450,
right?
Everything is at 450 kPa.
So T2 is somewhere in between 175 and 200
so interpolation, T2 minus 175, this difference,
divided by the total difference in temperature,
200 minus 175, should be this difference in
enthalpy divided by this difference.
And so I can solve for T2.
If I do that, I get 189.2 degrees C. Significant
figures I'm going to call this 190 degrees
C. So we have superheated steam and it's at
190 degrees C.
