Question $4.(20$ pts$)$ in a steady state pipe flow with no work and

negligible kinetic$-$and potential energy charges, heat is added

to the simple fluid $x$ through steps $a,$ b$,$ c$,$ end d as shown in the

figure. fluld at $50C$ and $1$MPa is heated to completely transform to

superheated vapor at $120C$ and $100$kPa. The enthalpy of the

fluld at point b$,$ Hb$,$ is geven as $40\frac{KJ}{\text{m}\text{o}\text{l}}$ and that at point c$,$ Hc$,$

is given as $80$ kj$/$moll at $70C.$

Fiuid $x$ follows the ideal gas equation of state both in the liquld

and wapor phesas and has constant specific heat given as CpL$/$R

$=9$ for the liquid and CpV$/$R $=4$ for the vapor.

Caiculate the total change in the entropy of $1$ mole of fluid $x$

from point a to d in J$/K.$