Question $1$

One lecturer and $99$ students continuously occupy a classroom $(20$ m long, $15$ m wide and $6$ m high$)$ between $7$ pm and $9$:$30$ pm$.$ The $C{O}_2$ generation rate from each person is $0\mathrm{.}005\frac{L}{s}.$ The outdoor $C{O}_2$ concentration is $400$ ppm $.$ The indoor $C{O}_2$ concentration at $7$:$00$ pm is $500$ ppm $.$ The mechanical ventilation rate is $10\frac{L}{s}$ in total for the classroom.

The infiltration rate can be neglected. It can be assumed that $C{O}_2$ concentration is uniform in the classroom being considered.

$(1)$ Calculate average $C{O}_2$ concentration in the classroom at $8$:$00pm$ and $9$:$30pm,$ assuming that both students and the lecturer all arrive at $7$:$00$ pm$.$

$(2)$ Discuss the likely indoor air quality condition and ventilation design in this classroom.