# 氣溫垂直遞減率

## 數學表示式

${\displaystyle \Gamma =-{\frac {dT}{dz}}}$

## 種類

### 乾絕熱垂直遞減率

${\displaystyle dP=-\rho gdz}$

${\displaystyle \delta Q=dU+\delta W=0}$

${\displaystyle mc_{V}dT+pdV=0}$

${\displaystyle PV=nR^{*}T}$

${\displaystyle PV=n(MR)T}$

${\displaystyle PV=mRT}$

${\displaystyle d(PV)=mRdT}$

${\displaystyle PdV+VdP=mRdT}$

${\displaystyle PdV=mRdT-VdP}$

${\displaystyle PdV=mRdT-\left({\frac {m}{\rho }}\right)dP}$

${\displaystyle mc_{V}dT+mRdT-{\frac {m}{\rho }}dP=0}$

${\displaystyle c_{V}dT+RdT-{\frac {dP}{\rho }}=0}$

${\displaystyle (c_{V}+R)dT={\frac {dP}{\rho }}}$

${\displaystyle c_{P}dT={\frac {dP}{\rho }}}$ [1]

${\displaystyle c_{P}dT={\frac {-\rho gdz}{\rho }}}$

${\displaystyle c_{P}dT=-gdz}$

${\displaystyle {\frac {dT}{dz}}=-{\frac {g}{c_{P}}}}$

## 參考

1. Marshall, John, and R. Alan Plumb. Atmosphere, Ocean and Climate Dynamics : An Introductory Text, Elsevier Science & Technology, 2007. ProQuest Ebook Central, https://ebookcentral.proquest.com/lib/cuhk-ebooks/detail.action?docID=534996.