1.

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

Answer»

`3//5`
`2//3`
`6//5`
`3//7`

Solution :Internal energy of n mole of an ideal gas at temperature T is GIVEN by
`U=(f)/(2)nRT` (f = DEGREES of freedom)
Given, `U_(1)` (Hydrogen) = `U_(2)` (Helium)
`therefore f_(1)n_(1)T_(1)=f_(2)n_(2)T_(2)`
`therefore (n_(1))/(n_(2))=(f_(2)T_(2))/(f_(1)T_(1))=((3)(2))/((5)(1))=(6)/(5)`
Here `f_(2)` = degrees of freedom of `He=3andf_(1)` = degrees of freedom of `H_(2)=5`


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