$6-167$ A refrigeration cycle is executed with R$-134$a under the saturation dome between the pressure limits of $1\mathrm{.}6$ and $0\mathrm{.}2$ MPa $.$ If the power consumption of the refrigerator is $3$ kW $,$ the maximum rate of heat removal from the cooled space of this refrigerator is

$($a$)0\mathrm{.}45k\frac{J}{s}$

$($b$)0\mathrm{.}78k\frac{J}{s}$

$($c$)3\mathrm{.}0k\frac{J}{s}$

$($d$)11\mathrm{.}6k\frac{J}{s}$

$($e$)14\mathrm{.}6k\frac{J}{s}$

$6-168$ A heat pump with a COP of $3\mathrm{.}2$ is used to heat a perfectly sealed house $($no air leaks$).$ The entire mass within the house $($air$,$ furniture, etc.$)$ is equivalent to $1200$ kg of air. When running, the heat pump consumes electric power at a rate of $5$ kW $.$ The temperature of the house was $7C$ when the heat pump was turned on$.$ If heat transfer through the envelope of the house $($walls$,$ roof, etc.$)$ is negligible, the length of time the heat pump must run to raise the temperature of the entire contents of the house to $22C$ is

$($a$)13\mathrm{.}5$ min

$($b$)43\mathrm{.}1$ min

$($c$)138$ min

$($d$)18\mathrm{.}8$ min

$($e$)808$ min

$6-169$ A heat engine cycle is executed with steam in the saturation dome between the pressure limits of $7$ and $2$ MPa $.$ If heat is supplied to the heat engine at a rate of $150k\frac{J}{s},$ the maximum power output of this heat engine is

$($a$)8\mathrm{.}1$ kW

$($b$)19\mathrm{.}7$ kW

$($c$)38\mathrm{.}6$ kW

$($d$)107$ kW

$($e$)130$ kW

$6-170$ A heat engine receives heat from a source at $1000C$ and rejects the waste heat to a sink at $50C.$ If heat is supplied to this engine at a rate of $100k\frac{J}{s},$ the maximum power this heat engine can produce is

$($a$)25\mathrm{.}4$ kW

$($b$)55\mathrm{.}4$ kW

$($c$)74\mathrm{.}6$ kW

$($d$)95\mathrm{.}0$ kW

$($e$)100$ kW