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| 1. |
Derive law of equipartition of energy |
| Answer» 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.Kinetic Energy of a single molecule: KE = 1/2 mv2. A gas in thermal equilibrium at temperature T, the average Energy is:Eavg = 1/2 mvx2\xa0+\xa01/2 mvy2\xa0+ 1/2 mvz2\xa0\xa0= 1/2KT + 1/2 KT + 1/2 KT = 3/2 KTwhere K = Boltzmann’s constant. In case of a monoatomic molecule, since there is only translational motion, the energy allotted to each motion is 1/2KT. This is calculated by dividing total energy by the degrees of freedom:3/2 KT\xa0÷ 3 = 1/2 KT | |