# 鋅銅電池

${\displaystyle {\rm {Zn_{(s)}+Cu_{(aq)}^{2+}\rightarrow Zn_{(aq)}^{2+}+Cu_{(s)}}}}$

## 熱力學理論

${\displaystyle \mathrm {d} U=T\mathrm {d} S-P\mathrm {d} V+{\mathcal {E}}\mathrm {d} Z}$

${\displaystyle \mathrm {d} U=T\mathrm {d} S+{\mathcal {E}}\mathrm {d} Z}$

${\displaystyle \mathrm {d} S=\left({\frac {\partial S}{\partial T}}\right)_{Z}\mathrm {d} T+\left({\frac {\partial S}{\partial Z}}\right)_{T}\mathrm {d} Z}$

${\displaystyle \mathrm {d} S=\left({\frac {\partial S}{\partial Z}}\right)_{T}\mathrm {d} Z}$

${\displaystyle \mathrm {d} U=\left\{{\mathcal {E}}+T\left({\frac {\partial S}{\partial Z}}\right)_{T}\right\}\mathrm {d} Z}$

${\displaystyle C_{T}^{(Z)}\ {\stackrel {def}{=}}\ {\frac {\mathrm {d} Q_{T}}{\mathrm {d} Z}}=T\left({\frac {\partial S}{\partial Z}}\right)_{T}}$

${\displaystyle \mathrm {d} F=\mathrm {d} U-\mathrm {d} (TS)=-S\mathrm {d} T+{\mathcal {E}}\mathrm {d} Z}$

${\displaystyle \left({\frac {\partial {\mathcal {E}}}{\partial T}}\right)_{Z}=-\left({\frac {\partial S}{\partial Z}}\right)_{T}}$

${\displaystyle \mathrm {d} U=\left\{{\mathcal {E}}-T\left({\frac {\partial {\mathcal {E}}}{\partial T}}\right)_{Z}\right\}\mathrm {d} Z}$

${\displaystyle \mathrm {d} U=\left({\mathcal {E}}-T{\frac {\mathrm {d} {\mathcal {E}}}{\mathrm {d} T}}\right)\mathrm {d} Z}$

${\displaystyle \Delta H=\Delta (U+PV)=\Delta U}$

${\displaystyle \Delta Z=zN_{A}e}$

${\displaystyle \Delta H=zN_{A}e\left({\mathcal {E}}-T{\frac {d{\mathcal {E}}}{\mathrm {d} T}}\right)}$

## 参考文献

1. ^ Daniell Cell. [2017-03-22]. （原始内容存档于2021-04-20）.
2. ^
3. ^ Colin B P Finn. Thermal Physics. CRC Press. 1992: 163. ISBN 0748743790.