$3\mathrm{.}16$ In Example $3\mathrm{.}15,$ it was demonstrated that refrigeration cycles utilizing a heat input to accomplish refrigeration tend to have a low $CO{P}_C,$ but a higher exergetic efficiency compared to vapor compression refrigeration cycles using electricity to run a compressor. Consider the combined cycle shown in Figure P$3\mathrm{.}16$ that utilizes a heat input to accomplish refrigeration.

The refrigerant used in the cycle is R$-143$m $($trifluoromethyl methyl ether$),$ an environmentally friendly refrigerant with low ozone depletion potential $($ODP$)$ and low global warming potential $($GWP$).($R$-143$m is one of the fluids available in EES.$)$ The R$-143$m enters the turbine at $1500$kPa,$100C,$ and expands to $500$ kPa $.$ The isentropic turbine efficiency is $86\%.$ After expansion, the refrigerant is fully condensed in the condenser. A pump with an isentropic efficiency of $64\%$ is used to raise the R$-143$m pressure back to the boiler pressure. At the condenser exit, the refrigerant flow splits; some going through the power loop just described, and the rest going through the refrigeration loop, where the SET is $-10C.$ The $R-143m$ exits the evaporator as a saturated vapor, after which it is compressed to the condensing pressure through a compressor with an isentropic efficiency of $75\%.$ The turbine delivers just enough power to run the compressor; there is no net power delivery from the cycle. The refrigeration capacity of the cycle is $80$ tons. Pressure drops through connecting piping can be considered negligible.

Determine the following parameters for this innovative heat$-$driven cycle:

a$.$ Mass flow rate of the refrigerant passing through the refrigeration loop $(k\frac{g}{s}).$

b$.$ Power required by the compressor $(kW).$

c$.$ Mass flow rate of the refrigerant passing through the power loop $(k\frac{g}{s}).$

d$.$ Heat transfer rate at the condenser $(kW).$

e$.$ Power draw of the pump $(kW).$

f$.$ Heat transfer rate required at the boiler $(kW).$

g$.CO{P}_C$ of the combined cycle.

h$.$ Draw a pressure$-$enthalpy diagram for R$-143$m and overlay the $9-$cycle state points on the diagram.

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Thermal Energy Systems: Design and Analysis

$3\mathrm{.}17$ Consider the cycle described in Problem $3\mathrm{.}16.$ The heat transfers in the cycle are occurring at boundary temperatures defined as follows:

$)=($ boiler boundary temperature $)=($ condenser boundary temperature $)=($ evaporator boundary temperature

For these conditions, determine the following:

a$.$ Exergy destruction rates in each of the components in the cycle $($kW$)$

b$.$ Exergetic efficiency of the cycle