Physics · Kinetic Theory · NEET
Yes. NCERT states this clearly: the average kinetic energy per molecule of any ideal gas is always (3/2) kBT and depends only on temperature, not on the nature of the gas. So at the same T, a light hydrogen molecule and a heavy oxygen molecule have EQUAL average kinetic energy. What differs is speed: to have the same (1/2)mv^2, the lighter molecule must move faster. Heavier molecule = lower rms speed, same energy.
No. The formula (3/2) kBT has no mass term. Mass affects the speed (vrms = sqrt(3kBT/m)), but not the energy. Two gases at the same temperature always share the same average kinetic energy per molecule regardless of how heavy each molecule is. Only temperature can change this energy.
(3/2) kBT is the average kinetic energy of ONE molecule. (3/2) RT is the total translational internal energy of ONE MOLE (that is, NA molecules) of a monoatomic gas. They are linked by R = NA x kB. So (3/2)RT = NA x (3/2)kBT. Use kB when you count per molecule, use R when you count per mole.
A molecule can move along 3 independent directions: x, y and z. By the law of equipartition of energy, each direction (each translational degree of freedom) carries an average energy of (1/2) kBT. Adding all three: (1/2)kBT + (1/2)kBT + (1/2)kBT = (3/2) kBT. The 3 comes from three-dimensional space, the 1/2 comes from each degree of freedom.
The average TRANSLATIONAL kinetic energy is (3/2) kBT for ALL gases, because every molecule can move in 3 directions. But TOTAL energy per molecule is larger for diatomic and polyatomic gases because they also rotate and vibrate. So translational KE = (3/2)kBT always, but total internal energy includes extra rotational and vibrational terms for non-monoatomic gases.
The average thermal energy for a mono-atomic gas is: (kB is the Boltzmann constant and T the absolute temperature)
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Average translational kinetic energy per molecule = (3/2) kBT, where kB = 1.38 x 10^-23 J/K and T is the absolute temperature in kelvin. Always use T in kelvin, never in Celsius.
No. It depends only on absolute temperature T. Changing pressure or volume at constant temperature does not change the average kinetic energy per molecule.
KE = (3/2)(1.38 x 10^-23)(300) = 6.21 x 10^-21 J per molecule. This value is the same for any ideal gas at 300 K, light or heavy.
They are directly proportional. KE = (3/2) kBT, so if absolute temperature doubles, the average kinetic energy per molecule also doubles. This is the kinetic interpretation of temperature.
E = (3/2) RT, since one mole has NA molecules and R = NA kB. For a monoatomic ideal gas this is also its total internal energy per mole.
