Equipartition of Energy

能量均分定理

The theorem of equipartition of energy states that molecules in thermal equilibrium have the same average energy associated with each independent degree of freedom of their motion and that the energy is

能量均分定理指出，处于热平衡的分子，其每个独立运动自由度所关联的平均能量相同，且能量

The equipartition result

serves well in the definition of kinetic temperature since that involves just the translational degrees of freedom, but it fails to predict the specific heats of polyatomic gases because the increase in internal energy associated with heating such gases adds energy to rotational and perhaps vibrational degrees of freedom. Each vibrational mode will get kT/2 for kinetic energy and kT/2 for potential energy - equality of kinetic and potential energy is addressed in the virial theorem. Equipartition of energy also has implication for electromagnetic radiation when it is in equilibrium with matter, each mode of radiation having kT of energy in the Rayleigh-Jeans law.

等效分配的结果在定义动能温度时很有用，因为这仅涉及平动自由度，但无法预测多原子气体的定压热容，因为加热这类气体时，内能的增加会将能量分配到旋转和可能的振动自由度中。每个振动模式将获得kT/2的动能和kT/2的势能——动能与势能相等在virial定理中得到阐述。能量的等效分配也对电磁辐射在与物质平衡时有影响，此时每种辐射模式在Rayleigh-Jeans定律中具有kT的能量。

For the translational degrees of freedom only, equipartition can be shown to follow from the Boltzmann distribution.

仅就平动自由度而言，可以证明能量均分定理源于玻尔兹曼分布。

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Average thermal energy 平均热能	Define constants 定义常量
Specific heats of solids 固体的比热容	Specific heats of gases 气体的定压比热和定容比热

Index

Gas law concepts

Kinetic theory concepts

索引气体定律概念气体动理论概念

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Thermal Energy

热能

The average translational kinetic energy possessed by free particles given by equipartition of energy is sometimes called the thermal energy per particle. It is useful in making judgements about whether the internal energy possessed by a system of particles will be sufficient to cause other phenomena. It is also useful for comparisons of other types of energy possessed by a particle to that which it possesses simply as a result of its temperature.

Define constants

定义常量

(The default mass of 18 amu, the mass of a water molecule, is used in the above calculation if you do not choose a value. The velocity of a water molecule at different temperatures is a good example of the molecular speeds associated with the internal energy of molecules.)

（如果未选择特定值，上述计算中默认使用18 amu的质量，即水分子的质量。水分子在不同温度下的速度是分子与内能相关速度的良好例子。）

The calculated thermal energy provides a useful comparison for the energies involved in other physical phenomena. For example, in the interaction of radiation with matter it is useful to compare the quantum energy of the photons of the radiation with the thermal energy at the existing temperature. The photon energy associated with the photons in a microwave oven at frequency 2.45 GHz is about 10^-5 eV. The average thermal energy at 20°C is 0.04 eV, about 3700 times higher. This suggests that the specific effects of the microwave photons in rotating molecules will be quickly randomized by the overwhelming thermal energy of the surroundings, so that the contribution of the microwaves will be "thermalized" or appear as a contribution to raising the temperature of the material.

计算出的热能为其他物理现象中涉及的能量提供了有用的比较。例如，在辐射与物质的相互作用中，将辐射光子的量子能量与现有温度下的热能进行比较是有用的。微波炉中频率为2.45 GHz的光子的能量约为10 -5 eV。20°C时的平均热能为0.04 eV，大约高3700倍。这表明微波光子对分子旋转的特定影响会被周围 overwhelming 的热能迅速随机化，因此微波的贡献会“热化”或表现为材料温度上升的贡献。

Molecular speed distribution for ideal gas

理想气体的分子速率分布

Fraction of particles above a certain energy

能量高于一定值的粒子比例

自由粒子所具有的平均平动动能，根据能量均分定理给出，有时也称为粒子的热能。它在判断质点系所具有的内能是否足以引起其他现象时很有用。它也用于比较粒子所具有的其他形式能量与由于其温度所具有的能量之间的差异。如果温度是 C = F = K = 10^ K，则平均‘热能’为 3kT/2 = eV = MeV = GeV 3kT/2= 10^ 焦耳 = 10^ 电子伏特。

中文译文中的待填/计算数值依次对应：1：tc 2：tf 3：t 4：tb 5：tp 6：ev 7：mev 8：gev 9：jb 10：jp 11：evb 12：evp。实际数值以上方原输入框为准。

Index

Kinetic theory concepts

索引气体动理论概念

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Internal Energy for Ideal Gas

理想气体的内能

Internal energy in general includes both kinetic energy and potential energy associated with the molecular motion. But the potential energy is associated with intermolecular forces and is presumed to be zero in an ideal gas where the only molecular interactions are the perfectly elastic collisions between molecules. Therefore the internal energy of an ideal gas is entirely kinetic energy.

While steam at 100 degrees Celsius is not strictly an ideal gas, the diagram illustrates the fact that the phase change to the gaseous state leaves only the kinetic portion of the internal energy. For a monoatomic ideal gas this internal energy is given by

If rotation and vibrational kinetic energies are involved (i.e. polyatomic molecules), then

如果涉及转动和振动动能（即多原子分子），则

虽然100摄氏度的蒸汽严格来说不是理想气体，但图示说明了相变到气态仅保留了内能的动能部分。对于单原子理想气体，其内能由

Study of the specific heats of gases provides evidence of whether or not rotation and vibration play a significant role in the molecular kinetic energy.

研究气体的定压热容可以提供证据，说明分子的旋转和振动是否在分子动能中起显著作用。

内能一般包括分子运动相关的动能和势能。但势能与分子间作用力有关，在理想气体中，分子间的唯一相互作用是分子间的完美弹性碰撞，因此势能被假设为零。因此，理想气体的内能完全由动能构成。

Index

Kinetic theory concepts

索引气体动理论概念

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