Answer:
[tex]S_{gen} = 18.519\,\frac{kJ}{K}[/tex]
Explanation:
Given that rigid tank is a closed system, the following model is constructed after the First Law of Thermodynamics:
[tex]W_{heater} + U_{sys,1} - U_{sys,2} = 0[/tex]
[tex]W_{heater} = U_{sys,2} - U_{sys,1}[/tex]
[tex]W_{heater} = m\cdot (u_{2}-u_{1})[/tex]
The entropy generation inside the rigid tank is determined by appropriate application of the Second Law of Thermodynamics:
[tex]S_{sys,1} - S_{sys,2} + S_{gen} = 0[/tex]
[tex]S_{gen} = S_{sys,2} - S_{sys,1}[/tex]
[tex]S_{gen} = m\cdot (s_{2}-s_{1})[/tex]
The properties of the steam are obtained from steam tables:
Intial State
[tex]P = 200\,kPa[/tex]
[tex]T = 120.21\,^{\textdegree}C[/tex]
[tex]\nu = 0.2222\,\frac{m^{3}}{kg}[/tex]
[tex]u = 1010.7\,\frac{kJ}{kg}[/tex]
[tex]s = 2.9294\,\frac{kJ}{kg\cdot K}[/tex]
[tex]x = 0.25[/tex]
Final State
[tex]P = 869.567\,kPa[/tex]
[tex]T = 173.88\,^{\textdegree} C[/tex]
[tex]\nu = 0.2222\,\frac{m^{3}}{kg}[/tex]
[tex]u = 2578.6\,\frac{kJ}{kg}[/tex]
[tex]s = 6.6332\,\frac{kJ}{kg\cdot K}[/tex]
[tex]x = 1.00[/tex]
The entropy change of the steam during the process is:
[tex]S_{gen} = (5\,kg)\cdot \left(6.6332\,\frac{kJ}{kg\cdot K} - 2.9294\,\frac{kJ}{kg\cdot K} \right)[/tex]
[tex]S_{gen} = 18.519\,\frac{kJ}{K}[/tex]
