Question 7.51: A 0.5 m^3 tank contains carbon dioxide at 300 K, 150 kPa is ...

C.V. The tank and the compressor.
Continuity Eq.4.15:            m _{2}- m _{1}= m _{ in }

Energy Eq.4.16:                  m _{2} u _{2}- m _{1} u _{1}={ }_{1} Q _{2}-{ }_{1} W _{2}+ m _{ in } h _{ in }

Entropy Eq.7.13:                m _{2} s _{2}- m _{1} s _{1}=\int d Q / T +{ }_{1} S _{2  gen }+ m _{ in } s _{ in }

Process:         Adiabatic    { }_{1} Q _{2}=0 ,         Process ideal  { }_{1} S _{2 \text { gen }}=0, \quad s _{1}= s _{ in }

Constant s so since the temperatures are modest use Eq.6.23

…………………………………….

Eq.4.15 : 1=\frac{\dot{m}_{1}}{\dot{m}_{3}}+\frac{\dot{m}_{2}}{\dot{m}_{3}}

Eq.4.16 : 0=\frac{\dot{m}_{1}}{\dot{m}_{3}} h_{1}+\frac{\dot{m}_{2}}{\dot{m}_{3}} h_{2}-h_{3}+\dot{Q} / \dot{m}_{3}

Eq.7.13 : \left(m_{2} s_{2}-m_{1} s_{1}\right)_{ c.v. }=\sum m_{i} s_{i}-\sum m_{e} s_{e}+\int_{0}^{t} \frac{\dot{Q}_{ c.v. }}{T} d t+{ }_{1} S_{2 gen }

Eq.6.23 : \frac{T_{2}}{T_{1}}=\left(\frac{P_{2}}{P_{1}}\right)^{(k-1) / k}