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Question : 9
Total: 14
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).
Solution:  
Here, atomic mass of argon M1=39.9
Atomic mass of helium He = 4.0
Let C1 and C2 be the rms velocities of argon and helium at temperature T1 K and T2 K respectively.
We know that rms speed is given by
C=√
3RT
M
 ;
C1=√
3RT1
M1
=√
3RT
39.9
 ;
C2=√
3RT2
M
=√
3R×253
4

Since C1=C2
√
3RT
39.9
=√
3R×253
4

⇒T=
39.9×253
4
=2523.7K
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