At what temperature is the "effective" speed of gaseous hydrogen molecules (molecular weight = 2) equal to that of oxygen molecules (molecular weight = 32) at $47^{\circ} C$ ?

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Solution

Effective speed is same as RMS speed since it determines the kinetic energy.

$v_{r m s} = \sqrt{\frac{3 R T}{M}}$

Thus, as per questionm

$\sqrt{\frac{T}{2}} = \sqrt{\frac{273 + 47}{32}} = \sqrt{\frac{320}{32}}$

$T = 20 K = {- 253}^{0} C$

Answer is ${- 253}^{0} C$

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At what temperature is the root mean square velocity of gaseous hydrogen molecules is equal to that of oxygen molecules at $47^{\circ} C$

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