Question
Question: According to Maxwell-Boltzmann distribution law of molecular velocities of gases, the average transl...
According to Maxwell-Boltzmann distribution law of molecular velocities of gases, the average translational kinetic energy is:
(A) 2KT per molecule
(B) KT per molecule
(C) RT per molecule
(D) 23KT per molecule
Solution
Recollect the concept of kinetic theory of gases and its postulates. Write the law of Maxwell-Boltzmann distribution for molecular velocities of gases. Take a look at all the options and then tick the correct option for translational kinetic energy of one molecule of gas.
Complete step by step solution:
- Kinetic energy is given as, K.E. = 21mv2 where m is the mass and v is the velocity.
- According to kinetic theory of gases, the kinetic energy of a gas is, K.E. = 21mvrms2 where m is the mass of a molecule of gas and vrms is the root mean square velocity of the gas which is equal to m3KT where K is the Boltzmann constant, m is the mass of a molecule of gas and T is the absolute temperature.
- If we substitute the value of root mean square velocity of a gas in kinetic energy equation we get, K.E.=21mvrms2=21m×m3KT=23KT.
- According to Maxwell-Boltzmann distribution law of molecular velocities of gases, at a given temperature, all the gas molecules irrespective of their masses, have the same average translational kinetic energy.
- Therefore, the average translational kinetic energy for a molecule is equal to 23KT where K is the Boltzmann constant and T is the absolute temperature.
Therefore, the correct answer is option (D).
Note: Remember according to Maxwell-Boltzmann distribution law of molecular velocities of gases, at a given temperature, all the gas molecules irrespective of their masses, have the same average translational kinetic energy which is equal to 23KT per molecule.