At 290 K, a nitrogen molecule exhibits an average translational kinetic energy of approximately 6.3 × 10^-21 J, illustrating the temperature-dependent nature of kinetic energy in accordance with the kinetic theory of gases.
The average kinetic energy of a nitrogen molecule in translational motion can be determined using the equation:
K = (3/2) * k_b * T
where K is the average kinetic energy, k_b is the Boltzmann constant (1.38 × 10^-23 J/K), and T is the temperature in Kelvin. Substituting the given values into the equation for a temperature of 290 K:
K = (3/2) * (1.38 × 10^-23 J/K) * (290 K)
K = 6.3 × 10^-21 J
The average kinetic energy of a nitrogen molecule's translational motion at 290 K is approximately 6.3 × 10^-21 J. This calculation exemplifies the relationship between temperature and kinetic energy as described by the kinetic theory of gases and underscores the microscopic nature of thermal motion in gases.