Ncert Exercises & Solutions

A gas mixture consists of 2.0 moles of oxygen and 4.0 moles of neon at temperature T. Neglecting all vibrational modes, calculate the total internal energy of the system. (Oxygen has two rotational modes.)

Hint: Use the concept of the law of equipartition of energy.

Step 1: Find the total energy of Oxygen.

Oxygen is diatomic gas having 5 degrees of freedom.

Energy (total internal) per mole of the gas

= \frac{5}{2} R T [R = U n i v e r s a l g a s c o n s \tan t, T = t e m p e r a t u r e]

For 2 moles of the gas, the total internal energy

= 2 \times \frac{5}{2} R T = 5 R T

...(i)

Step 2: Find the total energy of Neon.

Neon (Ne) is a monoatomic gas having 3 degrees of freedom.

∴

Energy per mole

= \frac{3}{2}

We have 4 moles of Ne.

Hence, Energy=

4 \times \frac{3}{2} R T

=6RT ...(ii) [Using Eqs.(i) and (ii)]

∴

Total energy = 5RT+6RT = 11RT

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