Internal energy of `n_(1)` mol of hydrogen of temperature `T` is equal to the internal energy of `n_(2)` mol of helium at temperature `2T`. The ratio `n_(1) // n_(2)` is

Options

A. `3/5`
B. `2/3`
C. `6/5`
D. `3/7`

Answer

C

Explanation

internal energy of a `n` moles of an ideal gas at temperature `T`is given by
`U = f/2nRT [f = "degress of freedom"0`
`U_(1)=U_(2)`
`f_(1)n_(1)T_(1)=f_(2)n_(2)T_(2)`
`:. (n_1)/(n_2) = (f_(2)T_(2))/(f_(1)T_(1)) = (3xx2)/(5xx1)=6/5`
Here, `f_(2)` = degree of freedom `He=3`.
and `f_(1)`= degrees of freedom of `H_(2)`=5`.