So let me pick up where we left off in the last video
some interested in deriving this %uh maximum efficiency limit for a solar
energy conversion
and this is a some time as soon as the Landsberg
limited and ahead basically
I you know mapped out %uh the energy and the associated
and Toby Flood fifth the energy flux say they are represented in this car
red the work is represented a in green and though the intro B-flat theory that
represented
in the blue or hair that take into account this factor
for a bite to eat which comes into play where the
radiative processor in viral in the energy transfer
and had also taken into account in this to a mission which has to take place
from this
said because they say there is a a safety at a finite temperature Tc stood
with him a dota
radiation as a black body as a said not this place is me a good
condition to derive death lines working amid and I and II stick to the basics so
Vista few stuff first and the second love
but there were dynamic to derive the third limit to let me right underfoot
love put them on it makes and this basis said the energy
a energy is the the in this conversion process
so I can now write down this energy conservation
as essentially this energy which is a
energy flux which is that coming from the Sun
this must be equal to on the
v8 at which workers pretty used bus
the rate at which a he does everyday tote from the system
loath close the flux associated energy flux associated with death
the a radiation coming from the stuff said
know the second I love for time when I makes it as as Lee
%uh relates the the fluxes a of entropy
and I can write again the in incoming flux
which I know no a the incoming flights due to the energy of the Sun which has
no I know how the factor of
for like three then this is my
incoming flux plus
member I do this the flag for other in kobe which was that generated a
in this conversion the
and that is going to be equal to the intro me which was a
which was %uh given out so they kobe which was associated with this
a blackbody radiation coming from the said that %uh the faceplate elated
to death energy flux up the radiation from the said
divided by that template so the said again that the factor of
for about a year ago the creative process or her
and then I want to admit that the energy they
Toby Flood associated with this heat which was a
here in our again I'm interested in the
fining the where are the efficiency of for this conversion
which I can again deposition by eat a and this is a again the
livor divided by the energy coming from the Sun
so I can now make you though the stuff for sale
and substitute for a WR her saw a substitute for W
as he s energy coming from the Sun
later the energy radiated out by the said
my with the heat
than this divided by yes
this is the efficiency which I can get from the third generation process
and this is the city no equal to
one minor if EC
by he with minus
you by he hath and I if I if the
look at this time there is basically a competitive the energy flux coming from
the said
divide that by energy flux a coming up from the Sun
and I know that I've treated aboard the said and the Sun
as up black body for the energy flux which are coming from these up black
bodies
I can the make you though the Stephen voicemail I'll
like is that the energy flux which is coming up from the Sun disproportionate
to the
fourth borrow the temperature the fun similarly to energy flux which is going
to be coming on it
from the said disproportionate to the fourth power of the
templates are the Fed and this is based on this writing down the
stephen was very low safer take this
two equations and then a good division up the the energy flux that leaves me
with the
that leaves me rather film which is proportional to the fourth power of the
temperature of the said
and divided by the fourth borrow the template or the Sun
against another leader lamb left to evaluate
is this cue delighted by yes
and I'm gonna make you love the second love for
what I lyrics to derive this I see that the that you don't your hair
and that is that yes to more here so
multiply or divide this aboard the left hand side and the right inside
buyer by by ES
and I C 88 00 its owner multiplied what the left hand side and that I'd inside
by
day so let me know that some were basically multiply
death by d a might apply
the might apply the left inside
does so by TA and then divide both the left and right inside by
yes and then we put a dot or
difficult to put it out there for some time the use this
dart on top of on top of this letter
and what it is you stood up and then is basically the startup is in the flux for
it's a Q&A noting he so cue died as
denoting the flux of he them over for good
do appoint them on but of throwed this analysis keep in mind that all these
don't have a dot
for theater don't bother them just you know something that I at the convention
that I like to use
so let me a it me simplify it does simplify it
so now what I get learn more to on my tight inside
is the stone cue by
the ES in there I get this
Excerpta or hair which is up plus
for by 3 be
see do it by he with
into he a divided by
DC the on the left inside a
a gay and I get a billion which is for my
3 EA by TAS
and then I get this extra tone which is that you to the intro PR generated
and what I want to do is a in this
in this %uh process what I want to do is a minimize this
value of well you off the hook you buy
yes and I am a.m. this from the situation it's clear that
that value would be minimal if the stone goes to the oh so if there's no
extra and go pee generated a in this process
do so to minimize this that you were you still I
assess the equate to the third on 20 and know what I get
is a on the value that I won't which has a
cue by he with
it's essentially equal to floor by
3 into a TA by TAS minus
a game for by 3 DA
by DC again I see this stone which is a
relating the energy flux the from the said
by and dividing it by the energy flux a other side and just I didn't dislike the
way I did it over here
I can you know the ratio these that do fluxes is related to the temperature of
the said
a and the temperature up the Sun and given by
for its power for the that temperatures
so no ever they say equation which creates more like you but he s
and I can plug that into my efficiency equation
so if I do that then the value of
efficiency that I get a century
%uh the idea of efficiency is no one minor if
dece by TS the too far
for in that are subject to this to a vote
from this equation so I substitute for minus
US by yes sir or her for that gives me minus
for by 83 EA by
DS and then a plus for by
3 DEA by beefy
and then do you feel about the earth race to the par-4
second take this term colon between the
this between these two tones and
then when I get to essentially efficiency
is a a given by Beth
equation where I can take place 53
by year with raised the bar for
the and that I get four but three
DA by the fee lawyers cell lines of combined
leave two tones and take them that the fee by if if the par-4
comin out said I know if I took it to the survey question
this basis the has a the temperature other Amy
with the affected other templates are the sandwiches
fix to as well and but also it has this temperature of the said
and that is the mostly coming into play and
this worked on so if I increase the temperature other said
this to increase this but on the other hand this
don't agree that different degrees is a in fact this term because a
less than one than this holding them North abstract
from the efficiency so in fact it or you can take a minimum
for this storm and in fact that though the road to be minimum when the
temperature above the said
is equal to the temperature of the area and that there are for make sense
because you know when the sedative that the democrats are they made that boorda
a good the your the energy flux Associated
love with the due to radiation from the said it would be a minimize
Secretary of makes and that United this value of
said they're very jittery would get the maximum efficiency
say 520 this value up for DC other democrats are the said it is equal to
the ambient temperature
then there's the equation as HD video says do
at that use this to 19 earth for by 3
DEA by the
s and then if I up stuff to do you dove for
DC equal to two years than this does become for it. and if I subtract the
one from it were only there for the won by three
fed won by 3 DC
by DS race to the bar in fact no
let me know it right don't give died at st.
a by TAS raised to the power
for and this is why risk I realized that I was going
it same part and never and that may protect our
in a box so our hair and the
best gives the to the maximum feeling love for
other efficiency that I can get from this took an Oreo
and if I put the value of 48 to be a a
to be 300 Karen at a value of TS to be
a 60 then carried so this gives me efficiency of
learn forgive it which corresponds to 93
bowing to 3 per se