热力学基础

热力学第一定律

\(Q=\Delta E+A\)

\(Q>0:系统吸热;\Delta E>0:系统内能增加;A>0:系统对外界作正功\)

气体的摩尔热容量

热容

\(C=\lim_{\Delta T\rightarrow 0}{\dfrac{\Delta Q}{\Delta T} }=\dfrac{dQ}{dT}\)

比热容\(C_b=\dfrac{dQ}{mdT}\):单位质量物质T升高一度所吸收的Q

摩尔热容\(C_m=\dfrac{dQ}{\nu dT}\):1mol物质T升高一度所吸收的Q

定容摩尔热容量\(C_{V,m}\)

\(C_{V,m}=\dfrac{(dQ)_V}{\nu dT}\)

\(dQ=dE+PdV,dV=0\Rightarrow C_{V,m}=\dfrac{(dQ)_V}{dT}=\dfrac{dE}{dT}\)

\(E=\dfrac{i}{2}RT\Rightarrow C_{V,m}=\dfrac{i}{2}R\)

定压摩尔热容量\(C_{P,m}\)

\(C_{P,m}=\dfrac{(dQ)_P}{dT}=(\dfrac{dE}{dT})_P+P(\dfrac{dV}{dT})_P=\dfrac{i}{2}R+R\)

单原子分子, $i = 3, C_{V,m}=3R/2, C_{P,m}=5R/2 \(, 双原子分子,\) i = 5, C_{V,m}=5R/2, C_{P.m}=7R/2 ,$ 多原子分子,$ i = 6, C_{V,m}=6R/2= 3R, C_{P.m}= 4R$

迈耶公式:\(C_{P,m}=C_{V,m}+R\)