For two gases `A` and `B` with molecular weights `M_(A)` and `M_(B)`, respectively, it is observed that at a certain temperature `T`, the mean velocity of `A` is equal to the `V_(rms)` of `B`. Thus, the mean velocity of `A` can be made equal to the mean velocity of `B`, if

Options

A. `A` is at temperature `T` and `B` is at `T'` such that `TgtT'`
B. Temperature of `A` is lowered to `T_(2)` while `B` is at `T` such that `T_(2) lt T`
C. Both `A` and `B` are raised to a higher temperature
D. Heat energy supplied to `A`

Explanation

To solve the problem step by step, we will analyze the relationship between the mean velocity of gas A and the root mean square (RMS) velocity of gas B, and then determine the conditions under which the mean velocities of both gases can be made equal.

### Step 1: Understand the formulas for mean velocity and RMS velocity
The mean velocity (u) of a gas can be calculated using the formula:
\[ u = \sqrt{\frac{8RT}{\pi M}} \]
where \( R \) is the universal gas constant, \( T \) is the temperature, and \( M \) is the molecular weight of the gas.
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