Solution: Click For PDF Version Data of the problem are
,
,
,
,
and
.
(a)
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

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