Okay, so last time we talked about a generic power cycle.
So, we need to have some arbitrary high-temperature reservoir to provide
heat transfer at a high temperature. We need some arbitrary low temperature
reservoir, what we're going to reject heat.
So, we have our heat transferred into our power cycle and we have our heat
transferred out of our power cycle. And then, we have our kind of black box
as it were. That is the power cycle itself and that's
going to be how we generate the work, or the power, out of this system.
So, where does a nuclear reactor fit? Well, if you aren't familiar with the
nuclear physics, the typical uranium reactors that we use in the United States
and most of the reactors around the world, those are used purely to generate
heat. So, the nuclear reaction itself is
incredibly exothermic, and an exothermic reaction is one that releases heat.
So, they have huge amount of heat that's released with each nuclear reaction in
those reactors. So, when we look at this generic
description, the nuclear reactor is the high-temperature reservoir.
And then, it's used to heat steam, so here's my little nuclear power plant,
those are the cooling towers which would actually be down here.
But to represent our nuclear power plant, here is where the reactions are
occurring. And again, that heat is then directed
into a steam power cycle. And we'll talk about those in detail in
just a couple of segments. But before we get into the details of
the, of the components, you know, what's the hardware in power plant?
What we want to talk about is how do we, what's the criteria for evaluating a good
power plant from a thermodynamics perspective?
So, what we're really talking about, what metric we're defining is the efficiency,
the thermodynamic efficiency of our power plant.
And so for a power cycle, the generic way that we define efficiencies is what you
want divided by what you paid for to get it.
So, in general, we would say our performance metric is what you want and
what did you paid for to get it. So, this is, you know, kind of a really
vague way of describing things. What do we mean by what did you pay for
to get it? Well, in the thermodynamic example, that
we have right here. What you paid for to get it was this heat
transfer. And if we want to be even more specific,
we can say, okay, well we know there's only so much heat transfer, that let's
say a ton of coal can, can provide. Or a ton of uranium, or a ton of natural
gas. So, we can be very specific on the heat
transfer from our particular heat source, okay.
So, that's what I paid for to get it. We're going to go ahead and, and call
efficiencies. We're going to use the Greek letter eta
here to represent the efficiency of a power plant.
And so, this is, we can put a p on it, just to show us, emphasize that this is
the efficiency. And so, that efficiency, we know that
what we paid for is this heat transfer. Okay, what we want out of the power plant
seems pretty obvious. It's the power, right?
So, that going to be the work out of the cycle.
Okay. Now, these energy transfers, these two
heat transfers, the high temperature and low temperature heat transfer and the
work transfer. Are all the energy transfers that we need
in order for us to make this heat engine, or this power cycle?
So, if we go ahead and apply a conservation of energy analysis to my
system here. So, this is my power plant, and we say,
again, you know, it's a closed system, the conservation of energy says, okay,
well I have to balance the internal energy.
The change, excuse me, in the total energy with the heat transfer, the net
heat transfer and the net work transfer. Well, again, it's a cycle.
So, by definition, the, there's no change in the energy in the system, so all I
have are these heat transfer and work transfer terms.
So, I'm going to, for cycles, this can get confusing.
So, I'm going to pause here and, and try and anchor people.
we're going to suspend our use of the sign convention for heat transfer and
works, work transfer. Or, maybe suspend isn't the right word.
We're going to impose what we already know should happen.
Okay. What does that mean?
Well, we know that the work transfer for the cycle, by definition, has to be equal
to the heat transfer. Net work transfer, net heat transfer.
Well, in my little generic description up here, I have the work for the cycle, and
I only have two heat transfers. If this work is out of the cycle, which
we want to be positive, then by definition the heat transfer into the
system has to be larger than quantitatively the heat transfer out of
the system. So, I'm going to write it like this.
And recognize, our sign convention would say, hey, Q out should have a negative
sign. But I'm already taking that into
consideration here. I've already imposed that negative sign.
So again, I guess you could say we're applying our sign convention on priority
and that these heat transfers and these work transfers are all going to be
absolute values. OK, so hopefully that doesn't disturb
people too much in terms of understanding the sign convention, we know there should
be work out. We know that the heat transfer in has to
be larger than the heat transfer out. Okay.
so then we take this information here, and you'll notice I'm moving back and
forth between heat transfer. And heat transfer rates, and we should be
completely flexible. Typically, we model these systems as
having one mass flow rate, so we can use either convention very easily.
If there's more than one mass flow rate in this system, then we have to be
cautious about moving back and forth. Interchangeably between work between
power and heat transfer rates, and work and heat transfer.
Okay, but we understand, hopefully we understand how to make those transitions
very well. Okay.
So, then we plug in this expression here. For changing everything into heat
transfer. I'll go ahead and put everything on a
rate basis here. And what we see is that the power, the
efficiency of my power plant is given by this very simple expression.
Okay, We also recognize for efficiencies 100%
is ideal and of course achievable. But this is kind of a typical definition
of efficiency. Right?
No one can be 100% efficient, as much as we'd like to be.
So, we recognize that there are bounds on the efficiency.
We have a lower bound of zero. We have an upper bound of one.
We also recognize, we'll never get to 100% efficiency.
So, we know that the power cycle, the range of the efficiency should be
somewhere between zero and 100%. And we'll talk about what sets the limit
for the best we could expect out of power plants.
that's also governed by very explicitly thermodynamics.
But under, by using some very advanced topics.
So, we're going to take the outcome of those advanced analysis, but we're not
going to discuss how the, the specifics of the analysis.
But it will give you the ability to take critical view of every power plant and
see what's the maximum efficiency you might achieve.