The root mean square (r.m.s) speed of the molecules of a rigid diatomic gas is 600 m s ⁻¹ . If the molar mass of the gas is 30 g mol ⁻¹ , the internal energy of one mole of this gas is

Step-by-step solution

The root mean square speed of a gas is given by: v_ rms = 3RT M Squaring and rearranging for RT gives: RT = M v_ rms ^2 3 For a rigid diatomic gas, the internal energy of one mole is: U = 5 2 RT Substituting the expression for RT into the internal energy equation: U = 5 2 ( M v_ rms ^2 3 ) = 5 6 M v_ rms ^2 The molar mass must be converted to SI units: M = 30 g mol ⁻¹ = 0.03 kg mol ⁻¹ Now, substitute the given values: U = 5 6 0.03 (600)^2 U = 5 6 0.03 360000 U = 5 0.005 360000 = 9000 J . Answer: 9000 J