An ocean thermal gradient power plant using a simple non$-$ideal Rankine Cycle operates with a peak boiler temperature of $\backslash (70^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash )$ and a condenser temperature of $\backslash (40^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash ).$ The warm surface water of the ocean is supplying the thermal energy to the boiler. Assume a high source temperature of $\backslash (80^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash ).$ The cooler water deeper in the ocean is the sink for heat rejection at the condenser. Assume a low sink temperature of $\backslash (35^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash )($Such a power plant is a type of solar plant. After all, it's the sun that heats the ocean surface water.$)$ Assume that the turbine has an isentropic efficiency of $0\mathrm{.}8$ and that the pump has an isentropic efficiency of $0\mathrm{.}75.$ Assume that the working fluid for the power plant is water. The quality of the steam leaving the boiler is $1\mathrm{.}0$ for a simple cycle. Find the following and present them on a single typed Summary page that is the front page of Part $1$: $1.$ The Net work per unit of mass flow rate of the plant's working fluid

$2.$ The plant's thermal efficiency

$3.$ Total entropy generation of each component $($deltaS$\_$system$+$deltaS$\_$surrounding$)$

$4.$ The back work ratio

$5.$ The required working fluid flow rate for a $1000$ MW net power output

$6.$ The diameter of the pipe leaving the boiler if the velocity in the pipe is to be $\backslash (100\backslash$mathrm$\{$ft$\}/\backslash$mathrm$\{$sec$\}\backslash )$