Question $3$

$($a$)$ A heat engine operates on a Carnot cycle and has a thermal efficiency of $\backslash (55\backslash \%\backslash ).$ The waste heat from this engine is rejected to atmosphere air at $\backslash (15^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ at a rate of $\backslash (800\backslash$mathrm$\{$~kJ$\}/\backslash$mathrm$\{$min$\}\backslash ).$ Determine:

$($i$)$ the temperature of the source, i$.$e$.,\backslash (\backslash$mathrm$\{$T$\}\_\{\backslash$mathrm$\{$H$\}\}\backslash )$;

$(2$ marks$)$

$($ii$)$ the power output of the engine;

$(3$ marks$)$

$($iii$)$ If the entire work output of the heat engine is used to drive a refrigerator that removes heat from the refrigerated space at $\backslash (-5^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and transfers it to the same ambient air at $\backslash (15^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ What is the maximum rate of heat removal from the refrigerated space?

$(5$ marks$)$

rigure

$($b$)$ Water in a piston$-$cylinder assembly, initially at a pressure of $100$ kPa and a quality of $0\mathrm{.}65,$ is heated at constant pressure to a temperature of $\backslash (200^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ The work done during the process is $300$ kJ $.$ Determine:

$($i$)$ the mass of water, in kg ;

$(4$ marks$)$

$($ii$)$ the heat transfer, in kJ ;

$($iii$)$ Plot the process in a $\backslash ($ p $\backslash )-$v diagram with respect to the saturation lines.