An
ideal gas experiences an adiabatic compression from ,
,
to ,
.
We have to calculate (a) the
value of ;
(b) the final temperature;
(c) quantity of gas present in moles; (d)
the total translational kinetic energy per
mole before and after the compression; and
(e) the ratio of the rms speed before to that
after the compression.
In an adiabatic process
pressure and volume vary as per the relation
(b)
In an
adiabatic process temperature and volume vary as per the relation
(c)
Amount
of gas in moles,
,
can be calculated from the ideal gas equation of state
(d)
Total
internal energy, which for monatomic molecules is equal to the total
translational kinetic energy, is given by
Therefore, the initial
total kinetic energy of the molecules of the gas is
The final total kinetic
energy of the molecules of the gas will be
(e)
Ratio
of the rms initial and final speeds of the molecules can be
calculated from the average kinetic energy of molecules at
temperature T , which
is given by the relation
where m
is the mass of molecules of the gas. We therefore have
,
,
to
,
.
We have to calculate (a) the
value of
;
(b) the final temperature;
(c) quantity of gas present in moles; (d)
the total translational kinetic energy per
mole before and after the compression; and
(e) the ratio of the rms speed before to that
after the compression.
,
,
,
,
.
,
can be calculated from the ideal gas equation of state
