The objective of this video is to introduce the concept of cycles that convert heat into
work and we will describe first the Carnot cycle which is going to be the best that we can do, the ideal
cycle, then describe the Rankine cycle which is a way of practically carrying out the same
process. So these are steady state cycles, and this is important, that we're running
a fluid around a cycle. So at any given point things don't change with time. So it's continuous
flow of a fluid. And an important term that we need to consider is the thermal efficiency.
And what this means, the symbol we often use, eta, is the net work, and we'll put absolute values so
we don't have to worry about signs, over the heat added to the system. So if the thermal
efficiency is less than one, essentially in a cycle you can imagine, this is what we have
to pay for, add energy, we have to burn something for example, and if you like this is what
we get out that we could sell. So some fraction of the heat can be converted into work. Well
the best that we can possibly do is to run a Carnot cycle, and perhaps it's easiest to
see when looking at a temperature versus entropy diagram. We have an isothermal step and then
adiabatic, this is adiabatic and reversible and therefore no entropy change. Then another
isothermal step at low temperature. So we are going around the cycle in this direction.
And then we return to our starting point with another adiabatic reversible step. So on a
pressure volume diagram, 1 to 2 is the isothermal, so this is high temperature, so this is where
we're adding heat at high temperature. 3 to 4 is the other isothermal step, it's at low
temperature so this is where we are removing heat, and then from 2 to 3 is the adiabatic expansion
so we are getting work out during the adiabatic expansion. And then from 4 to 1 we are putting
work back in at the other adiabatic compression. Assume these are all reversible steps, if so
then this area is going to be proportional to the work because we are looking at reversible
steps. So temperature/entropy diagram, this is where we add heat, get out work, put
in work and remove heat and we are running through the cycle in this direction. So turns
out for this Carnot cycle the efficiency, which remember is the net work over Qh is
just related to these two temperatures. So this is Th the high temperature, and this
is Tc, the low temperature. Well it turns out, for practical reasons we really can't
run a cycle like this, the way we run a cycle is, for example using steam and a Rankine
cycle. So what I've represented here on a T/S diagram is a Rankine cycle. Notice that
it approximates this Carnot cycle. Constant low temperature, part of the energy is added
at constant high temperature. So Qh is added here, Qc is removed here and so we are using steam
and so this blue line is the phase envelope where saturated liquid is on the left, saturated
vapor is on the right. And so we're adding heat here in a boiler. So step 1 to step 2. And
step 2 to 3 is we're getting work out so this is a turbine. We are getting work out with
a steam expanding through the turbine. I've shown the reversible case, if it were irreversible
then we would see entropy increase, and be, for example since we are going down to the
same pressure, this is a constant pressure, constant temperature line in the two phase
region. And then going from 3 to 4 is a condenser where we convert this vapor at low temperature
into a liquid. And then we can take the liquid, and this is a pump, where we increase the
pressure back up to the high pressure, because then we have a boiling at high temperature.
And then actually point one should be here, entering the boiler, heat it up to boiling
temperature, phase change at constant temperature. So I'll point out, when we go through the
turbine we're lowering the pressure, so it's a lower pressure at the exit, and it's a lower
temperature at the exit because we've taken energy out in the form of work and
therefore we've taken energy out of the steam. So we can apply the first law to each of these
steps in this Rankine cycle. We have a boiler in which delta H, because it's a flow system,
is equal to the heat added. Heat added is greater than zero. And then the turbine, work
is equal to delta H, and this is less than zero because we are taking energy out. The
condenser, Qc is equal to delta H and again delta H is negative where we are taking work
out. And then the work of the pump, well it's going to be delta H and that's a small number
turns out. V delta P, this is adding energy this is positive. I've drawn where, in the
diagram, we have the reversible case which is the vertical line, or this one is the irreversible
case. And so the work for the irreversible case is going to be some efficiency of the
turbine times the work for the reversible case. So this is different from the overall
efficiency of the cycle. This is due to the fact that we run it irreversibly, we need
to know something about the process we're running to the same final pressure but we
are going to end up not removing as much energy because the efficiency is less than one for
the turbine.