1. Initially, the translational rms speed of a molecule of an ideal gas is 465 m/s. The pressure and
volume of this gas are kept constant, while the number of molecules is doubled. What is the final
translational rms speed of the molecules?
Solution
Here ,
as P * V = n *R * T
if P and V is kept the same , for doubling the number of molecules , the temperature will be
halved
hence , the new temperature is half the old temperature
NOw, rms speed = sqrt(3 *R * T/molecular mass)
hence , rms speed will be 1/sqrt(2) times
new rms speed = 465/sqrt(2)
new rms speed = 329 m/s
final rms speed is 329 m/s