Question

the temperature at which the RMS velocity of helium is equal to the RMS velocity of methane at 127°​

Answer 1

The temperature at which the RMS velocity of helium is equal to the RMS velocity of methane at 127°​ is 100 K or $-173^0C$

Explanation:

The formula used for root mean square speed is:

$\nu_{rms}=\sqrt{\frac{3RT}{M}}$

where,  $\nu_{rms}$ = root mean square speed

R = gas constant

T = temperature

M = atomic mass

$T_{CH_4}=127^0C=(127+273)K=400K$

Now put all the given values in the above root mean square speed formula, we get:

$\nu_{rms}{He}=\nu_{rms}{CH_4}$

$\sqrt{\frac{3\times R\times T_{He}}{4}}=\sqrt{\frac{3\times R\times 400}{16}$

$T_{He}=100K=(100-273)^0C=-173^0C$

The temperature at which the RMS velocity of helium is equal to the RMS velocity of methane at 127°​ is 100 K or $-173^0C$

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