At what temperature is the root mean square speed of an atom in an argon gas 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).


All the three vessels have the same capacity, which implies they all have the same volume. Thus, each gas has the same pressure, volume, and temperature. According to Avogadro’s law, the three vessels will contain an equal number of the respective molecules.


Given:


Temperature of the helium atom(Th)


Th = –20°C = 253 K


Atomic mass of argon(Ma) = 39.9 u


Atomic mass of helium(Mh) = 4u


Let, Va be the rms speed of argon and let Vh be the rms speed of helium.


Since, MV2 = kBT (let kB be simply k)


V =


The rms speed of argon is given by-


Va = ---(1)


The rms speed of helium is given by-


Vh = ---(2)


since Va = Vh


=


=


Ta = Ma


Ta = × 39.9 u


Ta = 2.52 × 103 K


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


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