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Cp γ = c_p / c_v，c_v = c_p − R

Cp Cv Ratio

📐 计算公式

γ = c_p/c_v，c_v = c_p − R。空气 cp=1005、R=287 → γ≈1.40。

输入定压比热 c_p 与气体常数，求定容比热与比热比 γ。

定压比热 c_p (J/(kg·K))

气体常数 R (J/(kg·K))

Formula & Standard References

Item	Formula / Note	Source / Standard
Heat capacity ratio	γ = c_p/c_v	Thermodynamics
Mayer relation	c_p − c_v = R	Mayer relation
Degrees of freedom	γ = (f + 2)/f	Equipartition
Typical values	Monoatomic 5/3, diatomic 7/5	Gas data
Temperature effect	γ drops as vibration activates	Statistical thermodynamics
Engineering use	Speed of sound √(γRT/M)	Gas dynamics

📌 计算说明

γ = c_p/c_v，c_v = c_p − R。
空气 cp=1005、R=287 → γ≈1.40。

📐 Physical Constants

Constants used on this page and their authoritative sources, for verification and citation

Constant	Value	Unit	Source
Molar gas constant R	8.314462618	J·mol⁻¹·K⁻¹	New SI (derived from exact N_A·k)
Mayer's relation	c_p − c_v = R (per mole)	—	Ideal-gas thermodynamic identity
γ for a monatomic ideal gas	5/3 = 1.667	—	Equipartition theorem (3 translational d.o.f.)
γ for a diatomic ideal gas	7/5 = 1.400	—	Equipartition theorem (3 translational + 2 rotational)
Gas constant of dry air R_a	287.042	J·kg⁻¹·K⁻¹	Derived from R/M (CIPM 2007 dry-air M)

Note: γ falls as temperature rises (vibrational modes become excited) and depends on pressure for real gases; this page defaults to air with c_p = 1005 and R = 287, giving γ ≈ 1.40.

📚 深度解析：比热容比 γ

💡 常见使用场景

由定压比热 cp 与气体常数求定容比热 cv。
计算比热容比 γ=cp/cv 用于绝热过程。
理想气体各常数换算。

空气 cp=1005

cp=1005 J/kgK, R=287：cv=cp−R=718 J/kgK，γ=cp/cv=1005/718≈1.40。

双原子气体

常温双原子 γ≈1.4，单原子（氦）γ≈1.67。

❓ 常见问题（FAQ）

关系来源？: 理想气体 cp−cv=R，γ=cp/cv，三者知二推三。
温度影响？: 高温时 cp 略增，γ 略降，常温可视为常数。

比热比 γ 计算器