Law of Equipartition
class 11 physics
Answers
Answer:
Equipartition of energy, law of statistical mechanics stating that, in a system in thermal equilibrium, on the average, an equal amount of energy will be associated with each independent energy state.
Answer:
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According to the law of equipartition of energy, for any dynamic system in thermal equilibrium, the total energy for the system is equally divided among the degree of freedom.
The kinetic energy of a single molecule along the x-axis, the y-axis and the z-axis is given as
Law Of Equipartition,
=1/2mvx^2
along the x-axis
Law Of Equipartition,
=1/2mvy^2yrr
along the y-axis
Law Of Equipartition,
=1/2mvz^2
along the z-axis
When the gas is at thermal equilibrium, the average kinetic energy is denoted as
=1/2mvx^2
along the x-axis
=1/2mvy^2
along the y-axis
=1/2mvz^2
along the z-axis
According to the kinetic theory of gases, the average kinetic energy of a molecule is given by,
U1/2mv^2rms=3/2kbT
, where Vrms is the root mean square velocity of the molecules, Kb is the Boltzmann constant and T is the temperature of the gas.
The mono-atomic gas has three degrees of freedom, so the average kinetic energy per degree of freedom is given by
KEx=1/2KbT
If a molecule is free to move in space, it needs three coordinates to specify its location, thus, it possesses three translational degrees of freedom. Similarly, if it is constrained to move in a plane, it possesses two translational degrees of freedom and if it is a straight line, it possesses one translational degree of freedom. In case of a tri-atomic molecule, the degree of freedom is 6. And the kinetic energy of the per molecule of the gas is given as,
6xNx1/2KbT=3xR/NRKbT=3RT
Molecules of a mono-atomic gas like argon and helium has only one translational degree of freedom. The kinetic energy per molecule of the gas is given by
3xNx1/2KbT=3xR/NRKbT=3/2RT
The diatomic gases such as O2 and N2 which have three translational degrees of freedom can rotate only about their center of mass. Since, they have only two independent axis of rotation, as the third rotation is negligible, due to its 2-D structure. Thus, only two rotational degrees of freedom are considered. The molecule thus has two rotational degrees of freedom, each of which contributes a term to the total energy consisting of transnational energy t and rotational energy.
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