$(25$ points$)$ Consider a shower head and an electric resistance system as the control volume $($steady$-$flow system$)$ shown below. This system heats the water $(=1K\frac{g}{L})$ from $16C$ to $43C$ at a steady rate of $10\frac{L}{m}in.$ This system is connected to a heat exchanger for preheating liquid water before using the water head. Actually, water at $43C$ is to hot for taking a shower with.

$2\mathrm{.}1$ For an incompressible liquid water $($fluid$)$ with density $=1K\frac{g}{L}$ and specific heat capacity $c_p=4\mathrm{.}184k\frac{J}{K{g}^{o}C},$ the steady$-$state mass flow rate of water is $m^{}=0\mathrm{.}28K\frac{g}{s}.$

True False

$2\mathrm{.}2$ Assume that the heat exchanger is off. Treat the liquid water as an incompressible fluid with density $=1K\frac{g}{L},$ specific heat capacity $c_p=4\mathrm{.}184k\frac{J}{KgC}$ and assume a steady$-$state water flow. In this case, the required electric power input along with $T_1=16C$ is $W_{in}^{}=-18\mathrm{.}83kW.$

True False

$2\mathrm{.}2$ The entropy generation during steady$-$state liquid water flow along with $T_1=16C$ is approximately $S_{\text{g}\text{e}\text{n}}^{}=0\mathrm{.}3623k\frac{J}{K}$

True False

$2\mathrm{.}3$ The entropy generation along with $T_1=16C$ is $S_{\text{g}\text{e}\text{n}}^{}=0\mathrm{.}0623k\frac{J}{K}.$

True False

$2\mathrm{.}4$ If $T_1=30C,$ then the required electric power input is $W_{in,\text{n}\text{e}\text{w}}^{}=-9\mathrm{.}07kW$

True False

$2\mathrm{.}5$ The entropy generation along with $T_1=30C$ is $S_{\text{g}\text{e}\text{n}}^{}=0\mathrm{.}0293k\frac{J}{K}.$

True False