The mean kinetic energy of the molecules of an ideal gas at 399^ C is ' E '. The temperature at which the mean kinetic energy of its molecules will be ' E / 2 ', is

Step-by-step solution

The mean kinetic energy E of an ideal gas is proportional to its absolute temperature, given by E = 3 2 k_B T , where k_B is Boltzmann's constant. Given the initial temperature 399^ C , convert to Kelvin: T₁ = 399 + 273 = 672 K . At temperature T₁ , the energy is E ; we seek the temperature T₂ for energy E/2 . Using the proportionality E T , we have E₂ E₁ = T₂ T₁ . Substituting E₂ = E/2 and E₁ = E yields E/2 E = T₂ 672 K , so 1 2 = T₂ 672 K . Solving, T₂ = 672 K 2 = 336 K . Converting to Celsius: T₂ = 336 - 273 = 6