First law of thermodynamics - Thermodynamics Video Lecture - Class 11

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thermodynamics Path 8 is brought to you
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please make sure that you have watched
all the videos from part 1 to 7 before
going ahead with part 8 now that we are
clear with what is internal energy heat
and work now we can start this lesson
first law of thermodynamics because
first law of thermodynamics is nothing
but a relation between heat burn and
internal energy so let us see what does
the first law of thermodynamic state it
states that energy can neither be
created nor destroyed only transformed
to other forms we have studied
conservation of energy everywhere in all
energy conservation it says that energy
cannot be created or destroyed it can
only be transformed to other forms so
same is the true same is true even in
case of thermodynamics when we say this
we take the common examples of a ball
falling from the roof of a building what
happens when the ball is at the roof of
the building
it has only potential energy as it
starts falling down the potential energy
starts decreasing and the kinetic energy
starts increasing that means potential
energy is not getting lost rather it is
getting transformed to kinetic energy so
similarly we can take the example of
when we rub our hands together what
happens when we rub our hands the
kinetic energy or the mechanical energy
when we rub our hands gets transformed
into heat energy because of which if you
see that when you rub your hands for
quite a long time you tend to feel hot
right that's because the mechanical
energy when you move your hands together
you get converted into heat energy which
gives us the feeling of warmth so first
off thermodynamics states that sometimes
it appears to us that some kind of
energy is getting lost somewhere but
basically it is not getting lost
somewhere it is getting transformed to
some other form of energy now we will
see this was the logical expression of
first law of thermodynamics now we will
see the mathematical expression how is
first law of thermodynamics expressed or
defined mathematically first law of
thermodynamics is that if an amount of
heat say Delta Q is supplied to any
system let us suppose we have any system
this is my system and rest everything
else's surroundings right now suppose if
I supply an amount of heat say Delta Q
in this system then what happens this is
the input which I am giving to the
system and this system is doing some
amount of birth say there is a W on the
surroundings so this is the input which
I am giving to the system and this is
the output which is coming from the
system but it is observed that the
amount of heat which I am giving to the
system some part of the sleep is lost
and the remaining part is coming out as
work done on the surroundings so where
is this remaining part going this
remaining part is used up in increasing
the internal energy of the system so
what happens when I supply an amount of
heat Delta Q to the system the system
uses a small portion of this heat in
order to increase its own internal
energy right because whenever heat is
added to the system there will be some
change in temperature of the system so
that change in temperature will cause a
change in internal energy right because
internal energy is related to kinetic
and potential energy so when the
temperature increases the movement of
the molecules inside the system
increases so the total of so the sum of
kinetic and potential energy will also
change
the internal energy will also change so
when you up supply some amount of heat
to the system a small portion of that
heat is used up in increasing or
changing the internal energy of the
system and the remaining amount of field
is given out as well done on the
surroundings so here we say this is the
expression of first law of
thermodynamics Delta Q is equal to Delta
u plus Delta W where Delta Q is the heat
supplied to the system by the
surroundings Delta W is the work done by
the system on surroundings and Delta U
is the change in internal energy of the
system so this is our first law of
thermodynamics so what do we conclude
from the statement of first law of
thermodynamics let us look at that we
saw that first law of thermodynamics is
that Delta Q is equal to Delta u plus
Delta W so from this we can say that
Delta Q minus Delta W is equal to Delta
u now just before I started this topic
on first law of thermodynamics I told
you what is the difference between heat
world and internal energy I told that
heat and work are not state variables
whereas internal energy is a state wave
right I also told you that a state
variables a state variable is something
which depends only on the state of the
system it doesn't depend on how the
state is achieved so state variables are
path independent
right so they don't depend upon which
path was followed to reach that
particular state so this internal energy
is path independent but work done is
path dependent because well then is
nothing but a mode of transfer so how is
that work done is also important when we
talk about work
similarly heat flow is also
path-dependent because they are not
state variables so let us suppose that
we have a particular system let us
suppose we have a system whose initial
state is defined by these variables p1
v1 after some time the final state of
the system is defined by p2 v2 so for
the system in reaching from its initial
state to final state there was some
change in internal energy let us say
Delta u so this Delta u does not depend
on how the system changed from p1 v1 to
p2 v2 so internal energy only can is
concerned with the state of the system
at one particular time it has nothing to
do with how the states changed from
initial to final but if I talk about the
amount of work done in reaching the
initial to final state it depends on how
the system reached from initial to final
state so from this discussion we can say
that Delta U is path independent so we
can say that the difference of that is
Delta Q minus Delta W is part
independent so the the difference of two
path dependent quantities is path
independent
so this was one conclusion which we got
from the first law of thermodynamics
that even though heat and birth are two
path dependent quantities but the
difference of the two gives rise to a
path independent quantity now let us
look at certain special cases for
example
suppose that a system undergoes a
process such that Delta U is equal to
zero what do we mean when we say that
Delta U is zero that means there is no
change in internal energy of the system
the internal energy of the system
remains constant so in this case what
will happen the first law of
thermodynamic state is Delta Q is equal
to Delta u plus Delta W so Delta U is
equal to zero so we can say that Delta Q
is equal to Delta W that means the heat
supplied by the surroundings to system
should be equal to the heat it should be
equal to the work done by the system on
surroundings let us suppose this is my
system whatever amount of heat is given
to the system that much amount of work
should be done to the surroundings right
so that means whatever how much the
amount of input should be equal to the
amount of output there should be no loss
or no deduction anywhere right now let
us look at the second case it says that
let us suppose that system is a gas in a
cylinder with movable piston let us
suppose we have a cylinder somewhat like
this and it is fitted with a piston this
is a piston so you know what is a piston
right it is it is a kind of a movable
handle right so and here we have a gas a
gas is enclosed in this system and this
is the piston which can be moved
now since the piston is movable so by
moving the piston we can change the
volume of the gas right because if we
push the piston
very much downwards then the volume will
decrease similarly if we move it upward
the volume will increase so the piston
ring movable as we move the piston the
volume of the gas changes
and as the system as the piston is moved
there is some work
suppose if I move the piston downwards
there is some work done on the system
right so how do we define that work done
on the system as the piston is moved as
the piston is moved there is some work
done involved so that work done that is
Delta W will be given by we know that
what is what how did we define work work
was nothing but force into displacement
what is force in terms of pressure force
in terms of pressure is pressure into
area because pressure is nothing but
force by area so this is pressure into
area into displacement now what is area
into displacement area into displacement
is nothing but volume or the change in
volume which will take place right so
let us suppose that change in volume is
denoted by Delta V because as we move it
down so there will be some change in
volume involved so we can say that Delta
W can be written as the product of
pressure and the change in volume
therefore according to the first law
Delta Q is equal to Delta u plus Delta W
this can be written as Delta Q is equal
to Delta u plus P Delta P so this is the
form of the first law of thermodynamics
in case of a gas in a cylinder with
movable piston so these are two special
cases which are related to the statement
of first law of thermodynamics so I just
described them because if you understand
these kind of scenarios it will be
easier for you to solve numerical
problems because sometimes in numerical
problems you just just knowing the
statement of first law of thermodynamics
doesn't help you should also know how to
use the first law in different scenarios
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