Mu$$strame c$$mo resolver: The configurations shown below correspond to a cooling production system that will condense at $\backslash (30^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and evaporate at $\backslash (-20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ using the refrigerant R$134$a$.$

Take into account the following characteristics:

$-$ Cooling capacity generated in the evaporator of $25$ kW $.$

$-$ Refrigerant in saturation at the outlet of the condenser and evaporator.

$-$ The mass flow rate of refrigerant feeding the evaporator is $\backslash (0\mathrm{.}15\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash ).$

$-$ Consider the isentropic efficiency to be $0\mathrm{.}7$ and the mechanical$-$electrical efficiency to be $1.$

$-$ The volumetric efficiency of the compressors can be estimated with the relation $\backslash (\backslash$eta v$=1-0\mathrm{.}005\backslash$mathrm$\{$rp$\}\backslash ).$

$-$ Assume logical values as deemed appropriate.

Particular considerations for Configuration A:

$-$ Power exchanged in the external cooler of the compressors is $4$ kW $.$

$-$ The ratio between the flow rate circulating through the condenser and that injected between the stages of compression is $6\mathrm{.}66.$

$-$ The displacement volume of the low$-$pressure compressor is $68\mathrm{.}35\backslash (\backslash$mathrm$\{$m$\}^\{3\}/\backslash$mathrm$\{$h$\}\backslash ).$

Particular considerations for Configuration B:

$-$ Assume a logical intermediate pressure for the first stage of expansion.

Calculate for both Configurations A and B :

a$)$ The T$-$s and P$-$h diagrams of the system operation.

b$)$ Complete the table by first calculating the values of temperature, pressure, enthalpy, specific volume, and quality at each point.

c$)$ Mass flow rates of circulating refrigerants.

d$)$ Polytropic index for each compression.

e$)$ Power of each compressor.

f$)$ Energy efficiency of each cycle.

g$)$ Dimensions of the compressors if they are double$-$acting, with $2$ cylinders per compressor, $564$ rpm $,$ and a D$/$L ratio of $0\mathrm{.}5.$

h$)$ The condenser is cooled using fans with an area of $\backslash (4\mathrm{.}2\backslash$mathrm$\{$~m$\}^\{2\}\backslash )$ that move air at $\backslash (4\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$ Calculate the air outlet temperature if it enters at $\backslash (25^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$