1、Theorem of equipartition of energyTheorem of equipartition of energy Theorem of equipartition of energy1 The intrinsic energy of the ideal gas 22t12m v k T232 2 2212121z y xm m m v v v k T21 The average translational kinetic energy for each translational degree of freedon is2 k TSince the possibilit
2、ies for the movement along the x,y,z axis are equal,so For the equilibrium state with temperature T,each degree of freedom of matter(gas,liquid and solid)molecule shares the same kinetic energy,which readsThis conclusion is called Theorem of equipartition of energy.12k T The average translational ki
3、netic energy of a molecule reads1.Theorem of equipartition of energy(1)The theorem of equipartition of energy is a result from the statistical average for a large number of molecules,caused by the frequent collisions among moleculesExplanations(3)If a gas molecule has t translational degrees of free
4、dom,r rotational ones and s vibrational ones,the average total kinetic energy for each gas molecule reads1()2t r s k T The average potential energy for each molecule reads,so2sk T(2)Usually it also apply to liquid and solid.1(2)2 2it r s k T k T the average total energy for a gas molecule isFor rigi
5、d molecules(under normal temperature)0 s 1()2t r k T The intrinsic energy of gas:the summation of the heat movement kinetic energy for all the gas molecules,the vibrational potential energy between atoms in molecules and interaction potential energy among molecules2.The intrinsic energy of ideal gas
6、 The intrinsic energy of the ideal gas：the summation of kinetic energy for all the gas molecules and the vibrational potential energy between atoms in molecules.The intrinsic energy of 1mol of the ideal gas readsThe intrinsic energy of ideal gas reads with mass m and molar mass Mm readsm2m iU R TMm
7、A A2 2i iU N N k T R T explanation The intrinsic energy for the ideal gas with certain mass completely depends on the number of the degrees of freedom and the temperature of the gas,and it is irrelevant to the volume and the pressure of the gas.For a given gas,the parameter i is certain,so its intri
8、nsic energy only depends on the temperature,which agrees with the result of experimental observation.Joules lawMonatomic molecule gas,32V mC R Diatomic molecule gas,52V mC R Polyatomic molecule gas,3V mC R The molar heat capacity for the ideal gasThe molar heat capacity for ideal gas at certain volu
9、me,dd 2mV mU iC RT 2miU R T The molar intrinsic energy for ideal gas For the equilibrium state with temperature T,each degree of freedom of matter(gas,liquid and solid)molecule shares the same translational kinetic energy,which readsThis conclusion is called Theorem of equipartition of energy12k TThe intrinsic energy of 1mol of ideal gas readsThe intrinsic energy of the ideal gas with mass m and molar mass Mm readsm2m iU R TMm A A2 2i iU N N k T R T Thank you!
