Question

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).

Answer 1

Temperatureof the helium atom, T_He= –20°C=253 K

Atomicmass of argon, M_Ar= 39.9 u

Atomicmass of helium, M_He= 4.0 u

Let,(v_rms)_Arbe the rms speed of argon.

Let(v_rms)_Hebe the rms speed of helium.

Therms speed of argon is given by:

…(i)

Where,

Ris the universal gas constant

T_Aris temperature of argon gas

Therms speed of helium is given by:

…(ii)

Itis given that:

(v_rms)_Ar=(v_rms)_He

=2523.675 = 2.52 × 10³K

Therefore,the temperature of the argon atom is 2.52 × 10³K.