Kinetic interpretation on temperature Video Lecture - Class 11

hello friends this video on kinetic
theory part 16 is brought to you by
example.com no more fear from exam
please make sure that you have watched
all the videos from part 1 to part 15
before going ahead with part 16 now we
will study kinetic interpretation of
temperature that means what does kinetic
theory interpret about temperature it
says that the average kinetic energy of
a molecule is proportional to the
absolute temperature of the gas that
means the average kinetic energy is
proportional to absolute temperature now
now we will see how is it just now we
saw that the pressure of an ideal gas
according to kinetic theory is 1 by 3 m
into n DS where right now let us
multiply 3 on both sides so we get 1 by
3 m and V into V square but now let us
now let us suppose we multiply and
divide by 2 on our right hand side so we
get 2 by 3 n into n V by 2 v square but
so this can be written as 2 by 3 n into
V half M V squared by I am just
rearranging the terms nothing else so
what is this n into V what do you think
small n is n is number of moles or
number density so n is number of
molecules per unit volume that is number
density so n into capital V will be
equal to capital n that is number of
molecules so this will be n into 1/2 + v
square v now now look at the scale
so what is this capital n into half MV
square that means total number of
molecules multiplied by the kinetic
energy this is the number of molecules
in the gas sample number of molecules in
the sample of the gas and half MV square
is the average kinetic energy so this
becomes equal to PV is equal to 2 by 3 e
now based on this expression we will do
kinetic interpretation of temperature so
on the basis of this this forms the
basis of our kinetic interpretation of
temperature so this is the basis of
kinetic interpretation of temperature
now from ideal gas equation we know that
PV is equal to MU R T now what is Lim mu
is the number of molecules divided by
Avogadro's number what is at that is Kb
until Avogadro's number into T so from
this we know that PV is equal to n into
Kb T so this is one equation let us name
this equation as equation 2 and let us
call the previous equation as equation 1
now if you see that an F and side of
equation 1 and 2 are the same so we can
equate 1 and 2 because they both are
basically the same so we can say that 2
by 3 e is equal to n KP T or we can say
P is equal to 3 by 2 n KB T or we can
say e band and
that is the total energy average kinetic
energy but more is equal to 3 by 2 KB
into T now if you could pack this
equation what is this T by n is now
average tiny tick energy this is average
kinetic energy what is this 3 by 2 into
KB this is a constant we already know
that Boltzmann constant is a constant
for all gases and what does T T is our
absolute temperature so what do you see
you see that the average kinetic energy
is proportional to the absolute
temperature so absolute temperature is
the only factor that determines the
average kinetic energy of an ideal gas
so till now temperature was just a
measurable parameter of a gas which was
used to measure something but now this
measurable parameter has been converted
to a 1 into the quantity because
temperature has become equivalent to the
average kinetic energy so we can say
that temperature has been interpreted as
a molecular quantity so this is a very
important consequence of the kinetic
theory if you see in in the in one of
the first few slides I told you that
while is kinetic theory or success and
that I had mentioned that it gave
interpretation of it gave molecular
interpretation of temperature and
pressure this is what I meant it gave a
different recognition to his measurable
parameters temperature and pressure
thank you please visit exam few calm to
watch free educational videos try 3
online tests get the best quality study
materials study from the best tutors and
mentors and much more thank you once
again