Q$5$

A reversible heat engine operates between two reservoirs at temperatures of $\backslash (600^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and $\backslash (40^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ The engine drives a reversible refrigerator which operates between reservoirs at temperatures of $\backslash (40^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and $\backslash (-20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ The heat transfer to the heat engine is $2000$ kJ and the net work output for the engine refrigerator is $360$ kJ $.$

i$)$ Calculate the heat transfer to the refrigerant and the net heat transfer to the reservoir at $\backslash (40^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )[10$ marks$]$

ii$)$ Reconsider $($i$)$ above, given that the efficiency of the heat engine and the C$.$O$.$P$.$ of the refrigerator are each $40$ per cent of their maximum possible values $[10$ marks$]$