Consider a gas of triatomic molecules. The molecules are assumed to be triangular and made of massless rigid rods whose vertices are occupied by atoms. The internal energy of a mole of the gas at temperature T is :

Solution

Physics sir · 3 steps

A rigid triangle is a nonlinear molecule: 3 ways to move plus 3 ways to spin, so 6 degrees of freedom.

1. Translation. The centre of mass can move along x, y and z. That gives 3 translational degrees of freedom.
2. Rotation. The three atoms do not lie on one line, so the molecule has a real moment of inertia about all three axes. That gives 3 rotational degrees of freedom. The rods are rigid, so there is no vibration to count.

   U = f × 1/2RT = 6 × 1/2RT = 3RT

3. So. By equipartition each degree of freedom carries 1/2RT per mole. With f = 6, the internal energy is 3RT, option (d).

The idea to keep. Count degrees of freedom by shape: monatomic 3, linear rigid 5, nonlinear rigid 6. Multiply by 1/2RT per mole to get the internal energy.

Answer from the NTA final answer key. Solution by PrepWiser.