# 熱容量

（重定向自热容

## 定义

### 基本定义

${\displaystyle C=\lim _{\Delta T\to 0}{\frac {\Delta Q}{\Delta T}},}$

### 不同热力学过程下均相系统的热容量

#### 等压热容

${\displaystyle \mathrm {d} Q=\mathrm {d} U+P\mathrm {d} V.}$

#### 理想气体的热容量

${\displaystyle C_{P}-C_{V}=nR.}$
${\displaystyle C_{P}/C_{V}=\gamma ,}$

${\displaystyle n}$是气体的摩尔数，
${\displaystyle R}$氣體常數
${\displaystyle \gamma }$绝热指数（可以通过气体分子的自由度计算）。

${\displaystyle C_{V}={\frac {nR}{\gamma -1}},}$
${\displaystyle C_{P}=\gamma {\frac {nR}{\gamma -1}}.}$

## 单位

### 卡路里

• 1卡路里（亦称克卡路里、小卡路里）等同于4.184 J。該定義是为了使1克液态水的热容量为1 ${\displaystyle {\text{cal}}/^{\circ }\!{\text{C}}}$
• 1千卡路里（亦称千克卡路里、大卡路里，符号kcal或Cal）等同于1000 cal，即4184 J。1千克液态水的热容量为1 ${\displaystyle {\text{kcal}}/^{\circ }\!{\text{C}}}$

${\displaystyle 1\ {\text{cal}}/^{\circ }\!{\text{C}}=4.184\ {\text{J}}/{\text{K}}}$

${\displaystyle 1\ {\text{kcal}}/^{\circ }\!{\text{C}}=4184\ {\text{J}}/{\text{K}}.}$

## 负热容

### 恒星和黑洞

${\displaystyle U_{\text{pot}}=-2U_{\text{kin}}.}$

${\displaystyle U=-U_{\text{kin}}.}$

## 参考文献

1. ^ Halliday, David; Resnick, Robert. Fundamentals of Physics. Wiley. 2013: 524.
2. ^ D. Lynden-Bell; R. M. Lynden-Bell. On the negative specific heat paradox. Monthly Notices of the Royal Astronomical Society. Nov 1977, 181 (3): 405–419. Bibcode:1977MNRAS.181..405L. doi:10.1093/mnras/181.3.405.
3. ^ Lynden-Bell, D. Negative Specific Heat in Astronomy, Physics and Chemistry. Physica A. Dec 1998, 263 (1–4): 293–304. Bibcode:1999PhyA..263..293L. . doi:10.1016/S0378-4371(98)00518-4.
4. ^ Schmidt, Martin; Kusche, Robert; Hippler, Thomas; Donges, Jörn; Kronmüller, Werner; Issendorff, von, Bernd; Haberland, Hellmut. Negative Heat Capacity for a Cluster of 147 Sodium Atoms. Physical Review Letters. 2001, 86 (7): 1191–4. Bibcode:2001PhRvL..86.1191S. PMID 11178041. doi:10.1103/PhysRevLett.86.1191.
5. ^ See e.g., Wallace, David. Gravity, entropy, and cosmology: in search of clarity (preprint). British Journal for the Philosophy of Science. 2010, 61 (3): 513. Bibcode:10.1.1.314.5655 请检查|bibcode=值 (帮助). . doi:10.1093/bjps/axp048. Section 4 and onwards.
6. Cain, Fraser. How Cold Are Black Holes?. Universe Today. September 2, 2016.