I'm going to discuss some of the approaches you should use when solving problems, and
I'm going to do this in the context of a thermodynamics problem, a closed-system energy balance that
I'll use as an example. And so the problem statement is here, and of course the first
thing you want to do is read the problem statement, and read it more than once.
And then the next thing is to draw a diagram. So what I'm going to do first is pause, draw a diagram, and then
let's continue looking at how to solve this problem.
So notice that, when drawing the diagram, one of the things that's important is to list all the knowns and then the unknowns.
In this case we don't know the temperature and we don't know if liquid is present. So
we don't know if we have two phases or all vapor. Since we are adding heat at constant
pressure we are going to vaporize some liquid at least. And so this is the first step, we
have knowns, we have unknowns, and a diagram. So our second step then is to plan. In other
words, plan how we are going to do the solution before we do it. So this means picking a system.
In this case it's the water- all of the water whether it's liquid or vapor in the piston-cylinder.
And then this is an energy balance, so first law is the first thing we are going to do
for a closed system. And it's a closed system at constant pressure. So this means to solve
the first law we are going to need initial and final conditions so we're going to use
the steam tables to look up the properties of steam at different conditions. And then
we are going to determine: What is the final state? And that means temperature and phases
present. Now that we've planned out, let's actually do the solution.
That means first writing down the first law, which for a closed system: the change in internal energy is Q
plus W. Because it's constant pressure I'm using notation that the system does work and
energy is removed from the system. So constant pressure times delta V, and I'm going to rewrite
this as minus delta PV. The reason I'm doing this is because see I can now rearrange this equation
delta U plus delta PV is equal to Q. And delta U plus delta PV is equal to delta H. So this
means I can use delta H values from the steam tables and I know the value of Q. So delta
H is the final enthalpy per kilogram minus the initial enthalpy and that's going to equal
to Q which is 2000 kJ as is given in the problem statement, that's the amount of heat added.
So I'm going to go to the steam tables and for H1, because it's a mixture we do mass of the liquid times
enthalpy per kilogram of the liquid plus mass of the vapor, enthalpy per kilogram of the
vapor. So I'm going to write these numbers down and pause and fill in the numbers from
the steam tables. So H1, 851.1 kJ and this is for 1 kilogram. So notice when I wrote
the numbers down, I put the units in. This is very good practice to have the units in
always when solving problems. You can see the units cancel, we end up with kilojoules. So then our
energy balance says our H2 is H1 plus Q. So 2851.1 kJ is our final enthalpy. So
first thing we can do is, here is the saturated vapor enthalpy and this number is greater
than 2749. So we can conclude we have superheated vapor which is one of the questions we wanted
to answer. Now the question is: What is the temperature? So we go back to the steam tables,
the pressure stayed constant, enthalpy is 2851.1 kilojoules. So two properties of steam, single
component, uniquely determine this. And so we can go to the steam tables, and depending
on how accurate and how detailed our steam tables are we might have to interpolate, but
if we use detailed steam tables we can directly determine the temperature. Temperature for
this pressure, this enthalpy is 198 degrees C. And with significant figures we would call
this 200 degrees C. So an important aspect to solving problems of course the answer should
have units, should have correct number of significant figures and then we should check
is the answer reasonable. Is this a reasonable answer? Well if we look up the saturation
temperature at this pressure it's 151.9 degrees C and so 200 is greater than this, as we would
expect, we put energy in. We've put enough energy to vaporize all the liquid. That seems
pretty reasonable from the delta H of vaporization from the steam tables and so for this problem
there is not a lot of checking we can do but the checking that we do makes it look reasonable
and in general that's what we're looking for. Does this look reasonable? Do I get units
that are correct from the calculations? And so the idea, if you're systematic in solving
problems, always drawing a diagram, listing the knowns and unknowns, planning out the
solution before substituting in the numbers, you're more effective at solving problems.