Answer:511 K
Explanation:
Given
[tex]T_1=510^{\circ} C\approx 783\ K[/tex]
[tex]P_1=450\ KPa[/tex]
[tex]P_2=101\ KPa[/tex]
Power Produces [tex]W=50\ kJ[/tex]
For Polytropic Process
[tex]\dfrac{T_2}{T_1}=[\dfrac{P_2}{P_1}]^{\frac{k-1}{k}}[/tex]
For air [tex]k=1.4[/tex]
[tex]\dfrac{T_2}{T_1}=[\dfrac{P_2}{P_1}]^{\frac{k-1}{k}}[/tex]
[tex]\dfrac{T_2}{783}=[\dfrac{101}{450}]^{\frac{1.4-1}{1.4}}[/tex]
[tex]\dfrac{T_2}{783}=[\dfrac{101}{450}]^{0.2857}[/tex]
[tex]T_2=783\times 0.652[/tex]
[tex]T_2=510.94\ K\approx 511\ K[/tex]
(b)
[tex]W=\dot{m}c_p(T_1-T_2)[/tex]
[tex]50=\dot{m}\times 1.005\times (783-511)[/tex]
[tex]\dot{m}=\dfrac{50}{273.36}[/tex]
[tex]\dot{m}=0.183\ kg/s[/tex]
