热力学系统

开放系统

流动过程

${\displaystyle \mathrm {d} U=\mathrm {d} U_{in}+\delta Q-\mathrm {d} U_{out}-\delta W\,}$

${\displaystyle \delta W=\mathrm {d} (P_{out}V_{out})-\mathrm {d} (P_{in}V_{in})+\delta W_{shaft}\,}$

${\displaystyle \mathrm {d} U_{cv}=\mathrm {d} U_{in}+\mathrm {d} (P_{in}V_{in})-\mathrm {d} U_{out}-\mathrm {d} (P_{out}V_{out})+\delta Q-\delta W_{shaft}\,}$

${\displaystyle \mathrm {d} U_{cv}=\mathrm {d} H_{in}-\mathrm {d} H_{out}+\delta Q-\delta W_{shaft}\,}$

${\displaystyle {\frac {\delta W_{shaft}}{\mathrm {d} t}}={\frac {\mathrm {d} H_{in}}{\mathrm {d} t}}-{\frac {\mathrm {d} H_{out}}{\mathrm {d} t}}+{\frac {\delta Q}{\mathrm {d} t}}\,}$

封闭系统

${\displaystyle \Delta U=Q-W+m_{in}(h+{\frac {1}{2}}v^{2}+gz)_{i}-m_{out}(h+{\frac {1}{2}}v^{2}+gz)_{e}}$

${\displaystyle \mathrm {d} U={\delta Q}-{\delta W}.}$

${\displaystyle {\delta W}=P\mathrm {d} V.}$

${\displaystyle {\delta Q}=T\mathrm {d} S}$

${\displaystyle {\delta U}=T\mathrm {d} S-P\mathrm {d} V.}$

${\displaystyle \sum _{j=1}^{m}a_{ij}N_{j}=b_{i}^{0}}$

参考文献

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