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

c. Internal energy of `n` moles of an ideal gas at temperature ture `T`is given by
`U = (f)/(2) mRT` (f = degrees of freedom)
`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)) = (3 xx 2)/(5 xx 1) = (6)/(5)`
Here, `f_(2) = ` degrees of freedom of `He = 3`
and `f_(1) = ` degrees of freedom of `H_(2) = 5`