Question $13(4$ points$)$

A small room with the dimensions $\backslash (3\backslash$mathrm$\{$~m$\}\backslash$times $4\backslash$mathrm$\{$~m$\}\backslash$times $5\backslash$mathrm$\{$~m$\}\backslash ),$ the initial temperature of $\backslash (12\{\}^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and the initial pressure of $\backslash (100$ k P a $\backslash )$ is heated by a radiator with a total volume of $\backslash (0\mathrm{.}02\backslash$mathrm$\{$~m$\}^\{3\}\backslash )$ entirely filled with water at $200$ kPa and $\backslash (250^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ At the same time a fan is rotating at the speed of $100$ rpm under a torque of $\backslash (20\backslash$mathrm$\{$~N$\}.\backslash$mathrm$\{$m$\}\backslash )$ to circulate the hot air all over the room. After $20$ minutes, the pressure of the water inside the radiator is dropped to $75$ kPa due to its heat transfer to the room. The total heat loss of the room through the walls is $\backslash (6\backslash$mathrm$\{$~J$\}/\backslash$mathrm$\{$s$\}\backslash ).$ Determine:

a$)$ The water initial and final phase inside the radiator

b$)$ The heat energy generated by the radiator

c$)$ The net heat transfer to the air

d$)$ The final temperature of the air