A bar with an indoor volume of 2,000 m^3 has 250 smokers in it, each smoking 2 c

Question

A bar with an indoor volume of 2,000 m^3 has 250 smokers in it, each smoking 2 cigarettes per hour. An individual cigarette emits 1.5 mg of formaldehyde (HCHO). Formaldehyde converts to carbon dioxide with a reaction coefficient of k =0.4/hr. Fresh air currently enters the bar at a rate of 1,000 m^3/hr, while stale air leaves at the same rate. Assume 1 atm of pressure and 20degree C How does the result compare with the threshold eye irritation value of 0.05 ppmv? How big must the HVAC system be to meet or be below the threshold

Explanation / Answer

We have 250 smokers, each smoking 2 cigarettes per hour. Each cigarette emits 1.5mg HCHO.

Meaning in an hour 500 cigarettes are being smoked and amount of HCHO is 500*1.5=750mg/hr

Since complete mixing is assumed, the conc. Of HCHO C in the bar is same as the concentration of air leaving the bar. So,

Output rate = 1000 m3/hr * C(mg/m3) = 1000 mg/hr

And the decay rate is

Decay rate = KCV = (0.40/hr) * C * 2000 m3 = 800C mg/hr

Input rate = Output rate + Decay rate

750 = 1000C + 800C

C = 750/1800 = 0.416 mg/m3

In ppm   = (0.416 mg/m3) (24.45) / (molecular weight of HCHO)

              = (0.416 mg/m3) (24.45)/ (30.02)

               = 0.34 ppm(v)

As we can see the results are well above threshold eye irritation value of 0.05 ppm(v).

HVAC system with output rate around 11200 m3/hr should be installed.

750 = 11200 + 800

C = 750/12000 = 0.0625 mg/m3

                            = 0.05 ppm(v)

               

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