Control Mass

First Law of Thermodynamics:

d E = \sum δ Q - \sum δ W

m_{c v} (t) + δ m_{i n} = m_{c v} (t + δ t) + δ m_{o u t}

S_{c v} (t) + δ m_{i n} s_{i n}

S_{c v} (t + δ t) + δ m_{o u t} s_{o u t}

d S_{c m} = [S_{c v} (t + δ t) + δ m_{o u t} s_{o u t}] - [S_{c v} (t) + δ m_{i n} s_{i n}]

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

d S_{c m} \geq \sum \frac{δ Q}{T}

\frac{d S_{c m}}{d t} \geq \sum \frac{\dot{Q}}{T}