Answer:
(a) [tex]\Delta S_{ref}=3.876\frac{kJ}{K}[/tex]
(b) [tex]S_{heat\ source}=-1.678\frac{kJ}{K}[/tex]
(c) [tex]\Delta S _{tot}=2.198\frac{kJ}{K}[/tex]
Explanation:
Hello,
(a) In this case, such refrigerant, we can notice that at the given conditions, the initial entropy from property tables (Cengel 7th ed) is:
[tex]s_{initial}=s_f+xs_{fg}=0.15457+0.4*0.78316=0.4678\frac{kJ}{kg*K}[/tex]
Now, for the final condition, we first need to compute the initial specific volume as it remains the same (rigid tank) after the thermodynamic process:
[tex]v_{initial}=v_f+xv_{fg}=0.0007533+0.4*(0.099867-0.0007533)=0.0404\frac{m^3}{kg}[/tex]
Then, at 400 kPa we evaluate the given volume that is also between the liquid and vapor specific volume, thus, we calculate the quality at the end of the process:
[tex]x_f=\frac{0.0404-0.0007907}{0.051201-0.0007907} =0.786[/tex]
With it, we compute the final entropy:
[tex]s_{final}=0.24761+0.785*0.67929=0.781\frac{kJ}{kg*K}[/tex]
Finally, entropy change for the refrigerant turns out:
[tex]m_{ref}=\frac{0.5m^3}{0.0404\frac{m^3}{kg} }=12.4kg \\\\\Delta S_{ref}=12.4kg *(0.781\frac{kJ}{kg*K}-0.4678\frac{kJ}{kg*K} )\\\\\Delta S_{ref}=3.876\frac{kJ}{K}[/tex]
(b) In this case, by using the first law of thermodynamics we compute the acquired heat by the refrigerant from the heat source by computing the initial and final internal energy respectively (no work is done):
[tex]Q=\Delta U[/tex]
[tex]u_{initial}=38.28+0.4*186.21=112.764\frac{kJ}{kg}\\ \\u_{final}=63.62+0.786*171.45=198.40\frac{kJ}{kg}[/tex]
Hence:
[tex]Q=12.4kg*(198.40-112.764)\frac{kJ}{kg} =1059.1kJ[/tex]
Finally, the entropy change of the heat source (which release the heat, therefore it is negative):
[tex]S_{heat\ source}=\frac{1059.1kJ }{(358+273.15)K} \\\\S_{heat\ source}=-1.678\frac{kJ}{K}[/tex]
(c) Then, the total entropy change or the entropy generation for the process is:
[tex]\Delta S _{tot}=3.876\frac{kJ}{K}-1.678\frac{kJ}{K}\\\\\Delta S _{tot}=2.198\frac{kJ}{K}[/tex]
Which has thermodynamic agreement as it is positive
Regards.
