The average speed (actually the root-mean-square speed) of the argon atom is 432.8 m/s
The thermodynamic temperature T is proportional to the average kinetic energy of a molecule. The mean translational kinetic energy of an atom or (molecule) of an ideal gas is proportional to the thermodynamic temperature.
That is, the average speed (actually the root-mean-square speed)
1/2m[tex]c^{2}[/tex] = 3KT/2
Where
m = molar mass
c = speed
K = Bolzman constant
T = Temperature.
Given that the temperature of a argon atom is 27°C
Mass of an argon m = 6.63 x [tex]10^{-26}[/tex] Kg
Bolzman constant K = 1.38 x [tex]10^{-23}[/tex] J/K
Temperature T = 273 + 27 = 300K
Substitute all the parameters into the equation
1/2m[tex]c^{2}[/tex] = 3KT/2
m[tex]c^{2}[/tex] = 3KT
[tex]c^{2}[/tex] = 3KT/m
[tex]c^{2}[/tex] = (3 x 1.38 x [tex]10^{-23}[/tex] x 300) / 6.63 x [tex]10^{-26}[/tex]
[tex]c^{2}[/tex] = 187330.3
c = [tex]\sqrt{187330.3}[/tex]
c = 432.8 m/s
Therefore, the average speed (actually the root-mean-square speed) of the argon atom is 432.8 m/s
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