The document describes a gas with an initial translational root mean square (rms) speed of 465 m/s at constant pressure and volume. When the number of molecules is doubled while keeping pressure and volume constant, the temperature is halved according to the ideal gas law. As rms speed is directly proportional to the square root of temperature, doubling the molecules halves the temperature and reduces the rms speed to 465/√2 = 329 m/s.

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