In this screencast I will demonstrate how to calculate the enthalpy that occurs
before, during, and after a phase change. Lets start by looking at a phase diagram.
In particular that of water. Lets see what happens when we go from a liquid at 50 degree
C to a vapor at 150 degreeC at constant pressure in this case 1 atm. So the first thing that
we do is we raise the temperature from 50 degrees until we hit the boiling point or
100 degree C. Then as we change the phase from liquid to vapor we put in heat, but the
temperature pressure stay the same. That is because all the heat is going into changing
the phase. Now when the water is all vapor the temperature raises again as heat is continued
to be put in. Until we hit 150 degree C. So lets see how we can calculate that. So what
we are going to look at here is an evaporator, and we have right here liquid water, and 1
mole/sec is going in at 50 degree C. In the evaporator it is heated and vaporized, and
we have H2O vapor that comes out at 150 degree C, and this process will take place at a constant
pressure of 1 atm. In order for this to occur. We actually have 3 steps. So step 1 is that
we heat the liquid water from 50 degree C to the boiling point, which is 100 degree
C, and the reason we heat it to the boiling point to calculate the enthalpy is because
that is were the heat of vaporization is measured. This step here when heat is being put in to
change temperature is what is known as sensible heat. The second step is the phase change,
and this is were all the liquid water vaporizes until we have water vapor left, and this is
what is known as latent heat, and while this is occurring there is no change in temperature
or pressure. Finally step 3 is we are going to heat the H2O vapor from 100 degree C to
its final T 150 degree C, and this is also sensible heat. So lets start by step 1, and
in order to find the sensible heat we use what is known as the heat capacity, and this
is often called Cp. This is defined as the amount of heat needed to raise the temperature
of the substance by a certain amount. The way find the sensible heat is to integrate
this heat capacity from our starting temperature. In this case 50 degree C to our boiling temperature,
and we integrate the heat capacity of liquid water, which is in this case 75.4x10^-3 kJ/mol*degree
C. So when we calculate this and we are going to call this our H1. It equals 3.765 kHJ/mol.
That is the enthalpy of our first step. Our second step is that phase change, and for
that we use the heat of vaporization that is looked up at 100 degree C, and that is
equal to 40.656 kJ/mol, and we are going to call this H2. Our third step also involves
sensible heat so we use a heat capacity. However we are going to have to take the integral
from 100 degree C to 150 degree C, and now we are going to have to use the heat capacity
of the vapor., which is slightly more complicated then that of the liquid, and when we calculate
this it will equal 1.722 kJ/mol. Often to simplify things we truncate after the first
term, and if we done that instead. We would have ended up with 1.673 kJ/mol. Finally we
add them all up to get our final enthalpy. Why can we add up all these enthalpies, because
enthalpy is what is known as a state function. All we care about is the initial and the final
state of the enthalpy. We don't care what path we went through to get there, and so
even if this physically is not what is happening in the system. We can put together hypothetical
paths that we know the enthaplies for, and calculate the difference in enthapies, and
this entire thing is multiplied by 1 mole/sec, and when we do that we end up with 46.1 kJ/s
or 46.1 kW. One thing to notice is when we are calculating this enthalpy is how much
of the energy is caused by the latent heat of heat of vaporization. So when you are calculating
an energy balance that has a phase change in it. It is essential that you add that latent
heat to get the correct answer.