Carnot Cycle - Thermodynamics, Physics, Class 11 Video Lecture

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let us look at the steps of the sequence
of steps constituting one cycle of
Carnot engine so the first one is
isothermal expansion of gas right the
second step was adiabatic expansion of
gas the third step is isothermal
compression of gas and the fourth step
is adiabatic compression of gas now for
each of them there will be some work
done by the system I discussed in I
discussed all these things when I told
you about isothermal process and
adiabatic process we discussed about the
work done building an isothermal
expansion the work done during adiabatic
expansion
similarly isothermal compression and
adiabatic compression so if you want you
can write down the expressions for work
done for each of these processes so that
much amount of work has to be done for
isothermal expansion and erratic
expansion followed by compressions now
if we want to plot this graphically so
how will we get how will be plotted
graphically so let us write down the
expressions for each of these processes
so during isothermal expansion of the
gas work this work will be done by the
gas and heat is absorbed by the gas
length so in this case what will be the
work done work done will be nothing but
mu ad t1 l-n v2 by v1 we have derived
all these expressions in our previous
slide slide
so during isothermal expansion what
happens work done by the gas similarly
when there is adiabatic expansion of the
gas even during that his work is done by
the gas so in this case what is the work
done let us call this w 1 let us call
this w 2 the world then in this case
would be what it will be nothing
the expression for adiabatic change that
is ad divided by gamma minus 1 t1 minus
t2 right now during isothermal
compression work is done on the gas
because of this case heat is released by
the gas right so work is done on the gas
so in this case W 3 will become mu R t2
Ln v3 by v4 right now I will also tell
you about the change of state which
takes place in the first place let us
suppose that initially the gas is at the
state p1 v1 t1 so if this was the
initial state right so here what happens
the gas reaches from in the first step
what happens the change takes place from
p1 v1 p1 to p2 v2 t1 because it takes
place isothermally now in the second
case what happens the change takes place
from p2 v2 P 2 V 2 T 1 2 T 3 V 3 T 2
right now the temperature changes from
t1 to t2 pressure and volume also
changes to different values that is P 3
V 3
now in the third step the heat is
released to the cold reservoir that is
some work is done on the gas and again
it takes place isothermally that means
temperature will remain same here so
here what will happen from P 3 V 3 T 2
it will reach some value say P 4 V 4 t2
right then again during the last step
what will happen adiabatic compression
here also heat is released so work is
done on the gas
the work done will be given by R divided
by gamma minus one so the temperature
will change again so in this case the
state will change from P 4 V 4 T to 2 it
will change back to P 1 V 1 T 1 so that
means this will become R divided by
gamma minus 1 T 1 minus T 2 so this is
how the time out cycle takes place I
hope you understood what are the various
processes that constitute the Carnot
cycle now with the help of this we can
calculate the total work done involved
in case of a Carnot engine these are the
work done for each of the cycles so if
you want to find out the total work done
you can just add them all and find out
the total work done and once you know
the total work done you can even
calculate the efficiency of the Carnot
engine which will be nothing but the
total work done divided by the amount of
heat that is supplied that is W divided
by q1 so if you talk about that work
done the net work done or total work
done you can get that total work done by
adding these 4 that is W 1 plus W 2
minus W 3 minus W 4 that's because W 3
and W 4 represents heat that is released
so they are with negative signs so this
way you can get the total work done and
if you want to find out the efficiency
that is ETA for a Carnot engine so that
efficiency becomes this total work done
W divided by the amount of which it
takes from the hot reservoir that is q1
so this value will give the efficiency
of the Carnot engine so I leave it to
yourself to find out what you get as the
she of Carnot engine but I will tell you
the result of course so the efficiency
of Carnot engine comes out to be 1 minus
t2 by t1
this would become the efficiency of
Carnot engine I explained to you the
meaning I explained you the main portion
now your job is to add all of these work
done and then find out the efficiency
and reach this conclusion so this is
according to second law of
thermodynamics this is the maximum
efficiency that a heat engine can have
which is operating between two
temperatures t1 and t2 now let us see
how do we graphically describe Carnot
cycle so we plot a graph between
pressure and volume let us say this is
pressure along Y axis and the volume
along x axis so what is the first
process that takes place the first
process that takes place is an
isothermal expansion so isothermal
process is somewhat like this in our
previous slides I have told you
isothermal curves looks somewhat like
this and the adiabatic curves looks
somewhat like this the only difference
being adiabatic curves and bit steeper
than isothermal curves right so this is
my isothermal process that means this
process is starting from this state that
is the initial state which is p1 v1 t1
and the final state of isothermal
expansion is p2 v2 t1 so the temperature
remains constant so this is my first
step the second step was adiabatic
expansion so adiabatic expansion means
the volume is again increasing so it
would be something like this so here you
if you see the volume is increasing from
this v2 to some other point that is v3
and the pressure is decreasing so this
is p3 v3
and t2 because the temperature will
increase at this point so this is my
step to what was the third step third
step was isothermal compression
compression means the volume should
decrease so the again it is an
isothermal curve so it should go
somewhat like this if you see the volume
is decreasing so it is reaching some
other point that is P 4 V 4 and T 2
because it is isothermal so the
temperature will remain constant and
then the last process is again adiabatic
compression so this is also a
compression so here also volume is
decreasing so here it goes back to the
original state so if you see this cycle
will keep continuing right so the chain
of processes chain of these four
processes will keep happening and thus
the Carnot cycle will continue and the
Carnot engine will keep function in this
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