A balloon has 5.0 mole of helium at `7^(@)C`. Calculate
(a) the number of atoms of helium in the balloon.
(b) the total internal energy of the system.

Explanation

Given number of moles of helium =5
`T =7^(@)C =7 +273 =280 K`
(a) Hence number of atoms (He is monoatomic)
= Number of moles `xx` Avogadro's number
`5xx 6.023 xx 10^(23)`
`=30. 015 xx 10^(23)`
`=3.0 xx 10^(24)` atoms
(b) Now. average kinetic energy per molecule `=3/2 K_(B) T`
Here `K_(B) = "Boltzmann constant "" ""(It has only 3 degrees of freedom")`
`:.` Total energy of all the atoms
= Total internal energy
`=3/2 K_(b) T xx `number of atoms
`=3/2 xx 1.38 xx 10^(-23) xx 280 xx 3.0 xx 10^(24)`
`=1.74 xx 10^(4)J`