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The carbon dioxide concentration in a room can be used to indicate air quality.

The carbon dioxide concentration in a room with persons can after a time - t - be expressed as
c = (q / n V) [1 - (1 / en t)] + (c0 - ci) (1 / en t) + ci (1)
where
c = carbon dioxide concentration in the room (m3/m3)
q = carbon dioxide supplied to the room (m3/h)
V = volume of the room (m3)
e = the constant 2.718.....
n = number of air shifts per hour (1/h)
t = time (hour, h)
ci = carbon dioxide concentration in the inlet ventilation air (m3/m3)
c0 = carbon dioxide concentration in the room at start, t = 0 (m3/m3)
With an approximately carbon dioxide emission from a person in an cinema 0.05 m3/h - the emission from 100 persons can be calculated to approximately 5 m3/h.
If a carbon dioxide concentration at start up and in the inlet air close to zero, the pollution concentration in a 500 m3 cinema after one hour and with one air shift per hour, can be calculated as:
c = ( (5 m3/h) / (1 h-1) (500 m3) ) [1 - (1 / e((1 1/h) (1 h))] + ((0 m3/m3) - (0 m3/m3)) (1 / e(1 1/h)(1 h)) + (0 m3/m3)
= 0.006 m3/m3
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