A vessel of volume V contains a mixture of 1 mole of hydrogen and 1 mole oxygen (both considered as ideal). Let `f_(1)(v) dv,` denote the fraction of molecules with speed between v and (v+ dv) with `f_(2)(v)dv`, similarly for oxygen . Then ,

Options

A. `f_(1)(v) +f_(2) (v) =f(v)`obeys the Maxwell's distribution law
B. `f_(1)(v),f_(2)(v)` will obey the Maxwell's distribution law separately
C. neither `f_(1) (v), " nor "f_(2) (v)` will obey the Maxwell's distribution law
D. `f_(2) (v) " and "f_(1) (v)` will be the same

Explanation

To solve the problem, we need to analyze the distribution of speeds of molecules in a mixture of hydrogen and oxygen in a vessel. Here’s a step-by-step solution:

### Step 1: Understand the System
We have a vessel of volume \( V \) containing a mixture of 1 mole of hydrogen (H₂) and 1 mole of oxygen (O₂). Both gases are treated as ideal gases.

### Step 2: Identify the Speed Distribution Functions
Let \( f_1(v) \) be the fraction of hydrogen molecules with speeds between \( v \) and \( v + dv \), and \( f_2(v) \) be the fraction of oxygen molecules with speeds in the same range.

...