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At what temperature is the root mean square speed of an atom in an argon gas cylinder is equal to the root mean square of a helium gas at -20℃

At what temperature is the root mean square speed of an atom in an argon gas cylinder is equal to the root mean square of a helium gas at -20℃

Grade:12th pass

1 Answers

Vikas TU
14149 Points
one year ago
Dear student 
Temperature of the helium atom, T He = –20°C = 253 K
Atomic mass of argon, M Ar = 39.9 u
Atomic mass of helium, M He = 4.0 u
Let, ( v rms ) Ar be the rms speed of argon.
Let ( v rms ) He be the rms speed of helium.
The rms speed of argon is given by:
(V rms )Ar = sqrt (3RTar/ Mar)
(V rms )He = sqrt (3RTHe/ M He )
Equating two equal 
Tar = T He /M He * Mar 
=> 253/4 * 39.9
=> 2.52 *10^3 K 
 

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