Control Volume

Often: fluid (liquid, gas, etc.), open volume

Procedure:

d m = \sum δ m_{i n} - \sum δ m_{o u t}

\frac{d m_{c v}}{d t} = \sum {\dot{m}}_{i n} - \sum {\dot{m}}_{o u t}

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d E_{c v} = δ Q - δ W_{c v} + h_{T, i n} δ m_{i n} - h_{T, o u t} δ m_{o u t}

\frac{d E_{c v}}{d t} = \dot{Q} - {\dot{W}}_{c v} + h_{T, i n} {\dot{m}}_{i n} - h_{T, o u t} {\dot{m}}_{o u t}

d S_{c v} \geq \sum \frac{δ Q}{T} + \sum s_{i n} δ m_{i n} - \sum s_{o u t} δ m_{o u t}

\frac{d S_{c v}}{d t} \geq \sum \frac{\dot{Q}}{T} + \sum s_{i n} {\dot{m}}_{i n} - \sum s_{o u t} {\dot{m}}_{o u t}

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{\dot{m}}_{o u t} = {\dot{m}}_{a i r} + {\dot{m}}_{f u e l}

First Law of Thermodynamics

w_{n e t} = q_{i n} + q_{l o s s} + q_{o u t}

q_{i n} = \frac{{\dot{m}}_{f u e l}}{{\dot{m}}_{o u t}} (h_{f u e l} - h_{a i r}) > 0

q_{o u t} = h_{a i r} - h_{o u t} < 0

Second Law of Thermodynamics

{\dot{m}}_{o u t} s_{o u t} \geq {\dot{m}}_{a i r} s_{a i r} + {\dot{m}}_{f u e l} s_{f u e l} + \frac{q_{l o s s}}{T}