In this screencast we will provide an overview of latent heat as well as look at how we can
use physical property data to help us with latent heat calculations. So the term latent
heat is used to describe heat transfer that is associated with a phase change, and specifically
a phase change at constant temperature and pressure. So by considering the phases, the
only variable that is changing we are differentiating latent heat from sensible heat, which is the
heat transfer associated with the change in temperature. The phase changes that we are
most concerned with in chemical engineering operations are the transition between the
solid and a liquid as well as a liquid and a vapor. The transition of a solid to a liquid
is obviously melting, and the change in specific enthalpy associated with that change is the
heat of melting, which is given the variable of H hat sub M. The transition between a liquid
and a vapor is vaporization, and the specific enthalpy change associated with that process
is the heat of vaporization. Both of these quantities the heat of melting and vaporization
are determined experimentally, but can usually be looked at in different references. They
are usually tabulated. You can easily find this in F&R in appendix B1. We can generally
find this in thermodynamic text books as well as Perries', and there tabulated as a function
of temperature and pressure. So it is important that these are specified when we look these
quantities up, and if we want to look at an example of how we can use this data. We can
look at a simple example of the vaporization of water. So in this case we want to calculate
the heat that is required to vaporize a 100 moles of water per second at 100 C, and atm
pressure. We also want to calculate the heat that is required to condense 100 mol/s at
100 and atm pressure as well. The vaporization process is illustrated here in the flow chart.
We are trying to calculate the latent heat. So we want Q in kJ/s, and we have a representative
data here. That was pulled from the appendix in F & R. So here the heat of vaporization
is shown as a function of temperature and pressure. We are at 100 C, and 1 atm. So the
heat of vaporization is 40.66 kJ/mol. If we want to calculate the latent heat. We can
start with the open system energy balance. In this case the open system energy balance
reduces to Q is equal to delta H, which is assuming that there is no work. We are neglecting
any changes in kinetic and potential energy. The heat of vaporization is given as a specific
quantity. Another words it is given to a per mole basis. So we can rewrite our energy balance
as Q is equal to n dot, which is the molar flow rate times our specific enthalpy change,
which in this case is the heat of vaporization. So plugging in our numbers here. We have 100
mol/s. for our molar flow rate. Our polish heat of vaporization is 40.66 kJ/mol. So in
this case Q is equal to 4,066 kJ/s or kW. In the second part of the problem we are asked
to calculate what the latent heat is to condense 100 mol/s of water at the same temperature
and pressure, which is simpler than it looks at first. For the condensation process we
done most of the work already. You will not find in thermodynamic text books a heat of
condensation, and if we think about what is happening in this particular case. As we change
phase from vapor to a liquid it is the exact opposite of the vaporization process, and
if we considered that the specific enthalpy is a state function. In other words it only
depends on the initial and final condition. We are using the same finial initial conditions
and reversing them. So the heat of condensation is equal to, but opposite in side of heat
of vaporization at the same temperature and pressure. So in this case for the heat of
condensation our energy balance is n dot times the opposite of the heat of vaporization.
So the latent heat to condense the same amount of water at the same temperature and pressure
is simply negative 4066 kJ/s. The same holds for the freezing process. It is equal to and
opposite in sign of heat of melting at the same temperature and pressure. To better understand
the heat of vaporization represents physically. We can relate that data that we were given
to a phase diagram for pure water. A schematic of the phase diagram is shown bellow. For
pure water which shows pressure vs temperature, and the region at which the different phases
exist. So here we have a solid at a higher temperature we have a liquid and at higher
temperature and low pressure we have a vapor, and the region that divides the liquid and
the vapor region is were the phase change occurs, and were we can maintain 2 phases
at equilibrium. So this pressure temperature line represents the vapor liquid equilibrium
were we can maintain 2 phases. We can us the conditions from our example to describe the
behavior of water on this diagram. So for example if we specify the pressure is atm,
and this diagram is not shown to scale. The diagram illustrates that there is 1 temperature
at which water will change phase between the liquid and the water. So we intuitively now
that this temperature is the boiling point at 100 degree C. If at atm pressure we are
at 99 degC we would maintain pure liquid. If we at 101 degC at atm we would maintain
pure vapor, but that atm pressure and 100 we can transfer phase between the liquid and
the vapor, and we can maintain both phases at equilibrium if we had a system of pure
water, and it is at this temperature and pressure and this region on the phase diagram that
the heat of vaporization is given. So the heat of vaporization specifically represents
the transition between liquid and the vapor phase at this point at this pressure and temperature
on the phase diagram. The diagram also shows for any pressure not only 1 atm, there is
only one temperature at which the phase change occurs. This is true for water as well as
any other pure species. If we change the pressure or if we change the temperature we are moving
up. If we are increasing along the vapor liquid equilibrium line. If we increase the temperature
and the pressure is not free to change independently. So if we specify the temperature at which
the phase change occurs the pressure is fixed as well. So it is not quintessential that
if we increase the temperature to 102 that the pressure changes as well. As we are increasing
the temperature we are increasing the pressure, and we are moving up along the vapor liquid
equilibrium curve for that particular species. The effect of the change in temperature, and
pressure for example of we increase we are increasing the pressure, and we are decreasing
the heat of vaporization. So as we increase the temperature it takes less energy to vaporize
the liquid to the vapor phase. If we go all the way up the vapor liquid equilibrium line
we will eventually reach the critical point. In other words Tc and Pc. The significant
of the critical point is that we no longer can maintain differential phases at equilibrium.
So we lose the ability to differentiate the liquid from the vapor phase, and instead we
have a super critical fluid that exhibits the properties of 1 phase. So as we approach
the critical point the heat of vaporization approaches 0. Were we can no longer maintain
2 distinct phases at equilibrium.