A balloon has 5.0 moles of helium at 7 °C. Calculate:

(a) the number of atoms of helium in the balloon.

(b) the total internal energy of the system.

Hint: The no. of atoms depends on the no. of moles and the kinetic energy depends on the temperature.
Given, number of moles of helium = 5
                      T = 7 °C = 7 + 273 = 280 K
Step 1: Find the no. of atoms.
(a) Hence, number of atoms (He is monoatomic)
                        = Number of moles x Avogadro's number
                        =5×6.023×1023
=30.015×1023
=3.0×1024 atoms
Step 2: Find the average kinetic energy.
(b) Now, average kinetic energy per molecule=32kBT
Here, kB = Boltzmann constant                      (It has only 3 degrees of freedom)
 The total energy of all the atoms
                           =Total internal energy
                           =32kBT×number of atoms
=32×1.38×10-23×280×3.0×1024
=1.74×104 J