Ncert Exercises & Solutions

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 \times 6.023 \times 10^{23}

= 30.015 \times 10^{23}

= 3.0 \times 10^{24} a t o m s

Step 2: Find the average kinetic energy.

(b) Now, average kinetic energy per molecule

= \frac{3}{2} k_{B} T

Here,

k_{B}

= Boltzmann constant (It has only 3 degrees of freedom)

∴

The total energy of all the atoms
=Total internal energy

= \frac{3}{2} k_{B} T \times n u m b e r o f a t o m s

= \frac{3}{2} \times 1.38 \times 10^{- 23} \times 280 \times 3.0 \times 10^{24}

= 1.74 \times 10^{4} J