The rms speed of a gas is 300 m/s at 150 K. At what temperature will the rms speed be 600 m/s?
**Specific heat relation** C_p - C_v = R for ideal gas per mole, Mayer's relation, due to work done at constant pressure, degrees of freedom include translational, rotational, vibrational, each quadratic term contributes ½ R to C_v. v_rms ∝ √(T), (v₂)/(v₁) = √((T₂)/(T₁)).(600)/(300) = √((T₂)/(150)), 2 = √((T₂)/(150)).Square both sides: 4 = (T₂)/(150), T₂ = 600 K. Substituting values gives 600 K, which matches expected kinetic theory result, confirming mean free path λ = 1/(√2 n π d²), ideal gas law P V = n R T and v_rms = √(3 R T/M) relations.
Ref: NCERT > Physics Book > Behaviour of Perfect Gas and Kinetic Theory > Degrees of Freedom and Molar Specific Heat