Question
If the absolute temperature of gas is increased by 300%, then by what percentage the r.m.s. velocity of molecules will increase?
Solution
According to the kinetic interpretaion of temperature, r.m.s velocity is directly proportional to square root of absolute temperature.
i.e., ... (1)
Let the initial temperature of gas be T.
If the temperature is increased by 300% then the temperature of gas becomes 4T.
So, using equation (1), we have
... (2)
Therefore, from equations (1) and (2), we have
vr' = 2vr
The r.m.s. velocity at 4T temperature is double the r.m.s. velocity at temperature T.
So, percentage increase in velocity is given by,
i.e., ... (1)
Let the initial temperature of gas be T.
If the temperature is increased by 300% then the temperature of gas becomes 4T.
So, using equation (1), we have
... (2)
Therefore, from equations (1) and (2), we have
vr' = 2vr
The r.m.s. velocity at 4T temperature is double the r.m.s. velocity at temperature T.
So, percentage increase in velocity is given by,
