Isothermal Process - Thermodynamics Video Lecture | Physical Chemistry

this video will discuss isothermal
processes in thermodynamics specifically
as it relates to the expansion and
compression of ideal gases okay so for a
monatomic ideal gas we showed in the
statistical mechanics playlist that the
internal energy is equal to three-halves
NRT or three halves in KT number of
moles times gas constant times
temperature or number of particles times
Boltzmann constant times temperature and
R equals and K so that's the
translational energy for a monatomic
ideal gas from statistical mechanics so
what we see here is that for this
particular type of ideal gas the
internal energy is directly proportional
to the temperature so during some
process the change in internal energy is
going to be proportional to the change
in the temperature so if we have some
process where the change in the
temperature is going to be zero then the
change in the internal energy of an
ideal gas is also going to be zero so
processes where the change in
temperature is equal to zero are called
isothermal processes ISO being the root
word for same and thermal as it relates
to temperature and/or heat all right so
we have that for an isothermal process
our temperature doesn't change for an
ideal gas if the temp if the temperature
doesn't change then the internal energy
doesn't change so the internal energy
change of a closed system is going to be
the heat plus the work that occurs
during that process which we've now said
is equal to zero so thus the heat that
occurs during an isothermal process is
equal to the negative work so for a
reversible isothermal expansion or
compression of an ideal gas we showed
that in the previous video that the
reversible expansion or compression of
an ideal gas the work that is done
during that process is equal to negative
NRT log V final over V initial
number of moles gas constant temperature
final volume of system and initial value
of volume of system so the heat that it
so we're doing work so whatever work we
do is negative NRT log V final over V
initial so the heat that we need to
input into the system or remove from the
system needs to be equal and opposite to
the amount of work that the system does
so if the system expands and does work
on the surroundings we need to add in
some heat to at to give the energy back
so that the process is isothermal and
the temperature doesn't change if the
gas gets compressed and work is done on
it then we need to release some heat to
the surroundings to make sure that the
gas doesn't increase its temperature or
its energy so the heat that we have
during that process during the
reversible isothermal expansion or
compression of an ideal gas is going to
be plus NRT times natural log of V final
over V initial number of moles of gas
gas constant temperature and our initial
and final volume of the gas