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第134行：
第134行： − 与经典的能量均分定理相反，在室温下，分子的振动运动对热容的贡献可以忽略不计。这是因为这些自由度是冻结的，因为能量本征值之间的间距超过了对应于环境温度的能量()。在下表中，这种自由度不予考虑，因为它们对总能量的影响很小。那么，只有平动自由度和转动自由度，以相等的数量贡献于热容比。这就是为什么对于单原子气体和对于室温下的双原子气体。+ 第142行：
第142行： − 然而，在非常高的温度下，按振动温度(θ < sub > vib </sub >)的顺序，振动运动是不可忽略的。+ 第150行：
第150行： − + − − − {| class="wikitable" − − { | class = “ wikitable” − − |- − − |- − − − ! − − ! − − − − ! Monatomic − − !单原子的 − − − ! Linear molecules − − !线性分子 − − − ! Non-linear molecules − − !非线性分子 − − − |- − − |- − − − | Translation (, , and ) − − | 翻译(，，和) − − | align="center" | 3 − − | align="center" | 3 − − | align = “ center” | 3 − − | align="center" | 3 − − − | align = “ center” | 3 − − − − | align = “ center” | 3 − − |- − − − |- − − − | Rotation (, , and ) − − | 旋转(、和) − − | align="center" | 0 − − − | align = “ center” | 0 − − | align="center" | 2 − − − | align = “ center” | 2 − − − | align="center" | 3 − − | align = “ center” | 3 − − |- − − |- − − − − | Total (disregarding Vibration at room temperatures) − − | 总计(不包括室温下的振动) − − | align="center" | 3 − − − | align = “ center” | 3 − − | align="center" | 5 − − − | align = “ center” | 5 − − | align="center" | 6 − − − | align = “ center” | 6 − − |- − − − |- − − − | Vibration − − | 震动 − − − | align="center" | 0 − − | align = “ center” | 0 − − − | align="center" | − − | align = “ center” | − − − | align="center" | − − | align = “ center” | − − |- − − − |- − − − | Total (including Vibration) − − | 总数(包括振动) − − − | align="center" | 3 − − | align = “ center” | 3 − − − | align="center" | 3N − − | align = “ center” | 3N − − − | align="center" | 3N − − | align = “ center” | 3N − − |} − − |} −
→Gas molecules 气体分子
Contrary to the classical equipartition theorem, at room temperature, the vibrational motion of molecules typically makes negligible contributions to the heat capacity. This is because these degrees of freedom are frozen because the spacing between the energy eigenvalues exceeds the energy corresponding to ambient temperatures (). In the following table such degrees of freedom are disregarded because of their low effect on total energy. Then only the translational and rotational degrees of freedom contribute, in equal amounts, to the heat capacity ratio. This is why =}} for monatomic gases and =}} for diatomic gases at room temperature.
Contrary to the classical equipartition theorem, at room temperature, the vibrational motion of molecules typically makes negligible contributions to the heat capacity. This is because these degrees of freedom are frozen because the spacing between the energy eigenvalues exceeds the energy corresponding to ambient temperatures (). In the following table such degrees of freedom are disregarded because of their low effect on total energy. Then only the translational and rotational degrees of freedom contribute, in equal amounts, to the heat capacity ratio. This is why =}} for monatomic gases and =}} for diatomic gases at room temperature.
与经典的'''<font color="#ff8000"> 能量均分定理</font>'''相反，在室温下，分子的振动对'''<font color="#ff8000"> 热容量</font>'''的贡献通常可忽略不计。这是因为这些自由度被冻结了，因为能量本征值之间的间隔超过了与环境温度（kBT）相对应的能量。在下表中，这些自由度均被忽略，因为它们对总能量的影响非常小。只有平移和旋转自由度对'''<font color="#ff8000"> 热容比</font>'''有些许贡献（等量）。这就是为什么在室温下，单原子气体{{mvar|γ}}={{math|{{sfrac|5|3}}}}和双原子气体{{mvar|γ}}={{math|{{sfrac|7|5}}}}的原因。
However, at very high temperatures, on the order of the vibrational temperature (Θ<sub>vib</sub>), vibrational motion cannot be neglected.
However, at very high temperatures, on the order of the vibrational temperature (Θ<sub>vib</sub>), vibrational motion cannot be neglected.
不过，在非常高的温度下，差不多在振动温度(Θ<sub>vib</sub>)的量级上，振动运动就不能忽略了。
Vibrational temperatures are between 10<sup>3</sup> K and 10<sup>4</sup> K.
Vibrational temperatures are between 10<sup>3</sup> K and 10<sup>4</sup> K.
振动温度在10 < sup > 3 </sup > k 和10 < sup > 4 </sup > k 之间。
振动温度在10<sup>3</sup> K和10<sup>4</sup> K之间。
{| class="wikitable"
{| class="wikitable"
|-
|-
!
!
! [[Monatomic]]
! [[Monatomic]]
! [[Linear molecule]]s
! [[Linear molecule]]s
! [[molecular geometry|Non-linear molecules]]
! [[molecular geometry|Non-linear molecules]]
|-
|-
| Translation ({{mvar|x}}, {{mvar|y}}, and {{mvar|z}})
| Translation ({{mvar|x}}, {{mvar|y}}, and {{mvar|z}})
| align="center" | 3
| align="center" | 3
| align="center" | 3
| align="center" | 3
| align="center" | 3
| align="center" | 3
|-
|-
| Rotation ({{mvar|x}}, {{mvar|y}}, and {{mvar|z}})
| Rotation ({{mvar|x}}, {{mvar|y}}, and {{mvar|z}})
| align="center" | 0
| align="center" | 0
| align="center" | 2
| align="center" | 2
| align="center" | 3
| align="center" | 3
|-
|-
| '''Total''' (disregarding Vibration at room temperatures)
| '''Total''' (disregarding Vibration at room temperatures)
| align="center" | 3
| align="center" | 3
| align="center" | 5
| align="center" | 5
| align="center" | 6
| align="center" | 6
|-
|-
| Vibration
| Vibration
| align="center" | 0
| align="center" | 0
| align="center" | {{math|3''N'' − 5}}
| align="center" | {{math|3''N'' − 5}}
| align="center" | {{math|3''N'' − 6}}
| align="center" | {{math|3''N'' − 6}}
|-
|-
| '''Total''' (including Vibration)
| '''Total''' (including Vibration)
| align="center" | '''3'''
| align="center" | '''3'''
| align="center" | '''3''N'''''
| align="center" | '''3''N'''''
| align="center" | '''3''N'''''
| align="center" | '''3''N'''''
|}
|}