Question B $(25$ Marks$)$

When sitting and doing light desk work, a $20-$year$-$old student exhales $C{O}_2$ at an average rate of approximately $2{10}^{-4}mo\frac{l}{s}.$ Suppose there are several students in a room with dimensions $3\mathrm{.}5m4\mathrm{.}7m2\mathrm{.}5m.$ This room has one ventilation fan that blows fresh air into the room at a variable rate. There is also one vent through which air leaves the room. Other than the fan and vent, the room is perfectly sealed.

Assume that the temperature and pressure in the room remain constant at $294$ K and $101$ kPa $,$ respectively. The fresh air enters at the same temperature and pressure. You may consider air to be a mixture of two ideal gases: $C{O}_2(44\frac{g}{m}ol)$ and a hypothetical gas with a molecular mass of $29\frac{g}{m}ol.$ The concentration of $C{O}_2$ in fresh air is $425$ ppm $.$ Assume that the air in the room is well$-$mixed. Note that $1ppmC{O}_2$ corresponds to one molecule of $C{O}_2$ out of one million air molecules, which is a mole fraction of ${10}^{-6}.$ Although respiration involves consumption of $O_2$ and production of $H_{2}O,$ neglect these components in your analysis. The students occupy a negligible fraction of the room's total voirme.

Answer the following questions:

Write the total mole balance and determine the number of moles of air in the room.

$(4$ marks$)$

Use a mole balance to determine how the mole fraction of $C{O}_2$ in the room $(y)$ changes depending on the fresh air flow rate in $($:$\frac{L}{s}\}$ and the number of students $(n_s)$ in the room. $(6$ marks$)$

Suppose there is one student in the room. Calculate the fresh air flow rate that is required to maintain a steady $C{O}_2$ concentration of $1000$ ppm $.(3$ marks$)$

Suppose one student is in the room and the $C{O}_2$ concentration is steady $(1000$ ppm $).$ If one more student enters the room and the air flow rate does not change, sketch the expected evolution of the $C{O}_2$ mole fraction over time. $(6$ marks$)$

How long after the entry of the second student can the concentration of $C{O}_2$ be considered steady? $(3$ marks$)$

Suppose that an artificial intelligence system has been designed to accurately count the number of people in the room. This sensor is used to vary the fan speed to maintain a specified $C{O}_2$ concentration in the room. Is this an example of feedforward or feedback control? Explain your answer. $(3$ marks$)$