The input values are the following
[tex]\left.T_{1}=350 K\right\ then[/tex]
[tex]h_{1}=350.49 \frac{k j}{k g}, s_{1}=1.85708 \frac{K j}{K g \cdot K}[/tex]
By using the energy equilibrium
[tex]\dot{E}_{i n}-\dot{E}_{o u t}=\Delta \dot{E}_{s y s t e m}=0[/tex] , [tex]\dot{E}_{i n}=\dot{E}_{o u t}[/tex]
we have[tex]T_{2}=297.2 K[/tex]
eq (1) [tex]\dot{m}\left(h_{1}+\frac{V_{1}^{2}}{2}\right)=\dot{m}\left(h_{2}+\frac{V_{2}^{2}}{2}\right)+\dot{Q}_{o u t}[/tex] ∴
[tex]0=q+h_{2}-h_{1}+\frac{V_{2}^{2}-V_{1}^{2}}{2}[/tex]
Now, for specific energy h2:
[tex]h_{2}=h_{1}-q_{o u t}-\frac{V_{2}^{2}-V_{1}^{2}}{2}[/tex]
By replacing the eq (1) we have
[tex]h_{2}=350.49 \frac{k j}{k g}-3.2-\frac{\left(320 \frac{m}{s}\right)^{2}-\left(50 \frac{m}{m}\right)^{2}}{2}\left(\frac{1 \frac{k j}{k g}}{1000 \frac{m^{2}}{s^{2}}}\right)[/tex]
[tex]h_{2}=297.34 \frac{k j}{k g}[/tex]
By using a standard ideal-gas properties of air we have
[tex]T_{2}=297.2 K[/tex]
