PROBLEM $5.(20$ POINTS$)$

a$.15$ points

An office has one external wall $5$ m long, containing a window of area $4m^2$; the width of tho office from the window to the wall adjacent to the corridor is $4$ m $,$ and the ceiling height is $3$ m There are similar offices above, below and on either side. The temperature in the corridor $i16C,$ the temperature in the room is $20C,$ and the external design temperature is $-1C.$ If the heat transfer coefficients for the external wall, window and internal wall are $1\frac{W}{m^2}K5\mathrm{.}6$ W$/$m ${?}^{2}K,$ and $2\mathrm{.}7\frac{W}{m^2}K,$ respectively, and an air change rate of one per hour is require for ventilation, calculate the heat input to the room.