Question

A vessel of volume V contains a mixture of 1 mole of hydrogen and 1 mole oxygen (both considered as ideal). Let f₁(v)dv, denote the fraction of molecules with speed between v and (v + dv ) with f₂(v)dv, similarly for oxygen. Then,(a) f₁(v) + f₂ (v) = f (v) obeys the Maxwell's distribution law(b) f₁(v), f₂(v) will obey the Maxwell's distribution law separately(c) neither f₁(v), nor f₂(v) will obey the Maxwell's distribution law(d) f₂(v) and f₁(v) will be the same

Answer 1

Answer:

A) Obey the Maxwell’s distribution law separately.

Explanation:

The vrms gives a general idea of the molecular speeds in a gas at a given temperature. However, this does not depict the speed of each molecule as vrms. Many molecules have speed less than vrms and many have speeds greater than vrms.  according to maxwell's equation the distribution of molecules in different speeds is -

dN = 4πN(m/2πkt)-3/2 v²edv

where dN is the number of molecules with speeds between v+dv

The masses of hydrogen and oxygen molecules are different.  Thus, for a function f(v), the number of molecules dn = f(v), The molecules that have a speed between v and v + dv.

The Maxwell-Boltzmann speed distribution function ( Nv = dn/dv depends on the mass of the gas molecules.  Hence, for each function f1(v) and f2(v), the n will be different, hence each function f1(v) and f2(v) will obey the Maxwell’s distribution law separately.