What temperature the RMS velocity of oxygen will be same as that of methane at 27 degree Celsius?

Given data:

Temperature of Methane Gas T2 = 27 degree celcius = 27 + 273 = 300K

At temperature T1, Vrms of Oxygen and Methane are equal.

To find: Temperature T1.

Solution:

We know that,

Root mean square velocity Vrms = sqrt(3RT/M)

Here,

M is the molecular mass of the gas.

R the gas constant.

T is the absolute temperature.  

Now, if Vrms of oxygen and methane are equal, then

sqrt(3RT1/M1) = sqrt(3RT2/M2)

T1 = (M1/M2) T2  

We know that,

Molecular mass of oxygen M1 = 32 g/mol

Molecular mass of methane M2 = 16 g/mol

So, T1 = (32/16 ) * 300 = 600K

answer is 600 Kelvin or 327 degree Celcius.

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At what temperature the RMS velocity of oxygen will be same as that of methane at 27?

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