$$ A well$-$insulated, non$-$rigid $3-$m $4-m6-m$ room initially at $7C$ is heated by the radiator of a

steam heating system. The radiator has a volume of $15$ L and is filled with superheated vapor at

$200$ kPa and $200C.$ At this moment both the inlet and the exit valves to the radiator are closed.

A $120-$W fan is used to distribute the air in the room. The pressure of the steam is observed to

drop to $100$ kPa after $45$ minutes as a result of heat transfer to the room.

$(2$a$)$ Determine the heat transfer from the steam radiator to the room after the $45$

minutes $(Q_{\text{s}\text{t}\text{e}\text{a}\text{m}\text{,}\text{o}\text{u}\text{t}}).$

$(2$b$)$ Assuming constant specific heats for air at room temperature $($Table A$2),$

determine the average temperature of air after $45$ minutes. Assume the air

pressure in the room remains constant at $100$ kPa and thus the air expands as it

is heated.

$*$Note: neglect the volume of the radiator in part $($b$)$ and assume that $V_{1,\text{a}\text{i}\text{r}}=346m$