Atwhat temperature is the root mean square speed of an atom in an argongas cylinder equal to the rms speed of a helium gas atom at –20 °C? (atomic mass of Ar = 39.9 u, of He = 4.0 u).
Temperatureof the helium atom, THe= –20°C=253 K
Atomicmass of argon, MAr= 39.9 u
Atomicmass of helium, MHe= 4.0 u
Let,(vrms)Arbe the rms speed of argon.
Let(vrms)Hebe the rms speed of helium.
Therms speed of argon is given by:
…(i)
Where,
Ris the universal gas constant
TAris temperature of argon gas
Therms speed of helium is given by:
…(ii)
Itis given that:
(vrms)Ar=(vrms)He
=2523.675 = 2.52 × 103K
Therefore,the temperature of the argon atom is 2.52 × 103K.