A house has cracks in the basement floor through which radon is emitted into the

Question

A house has cracks in the basement floor through which radon is emitted into the house.

The total volume of the house is 650 m3 (assume that it is well mixed throughout). The

radon source emits 250 pCi/s (pCi or picocuries, is a unit proportional to the amount of

radon gas, and indicates the amount of radioactivity of the gas). Air inflow can be

modeled is as a flow of clean air into the house of 722 m3/h, and the outflow is equal to inflow.

(a) What is the steady-state concentration of radon (in pCi/L) in the house if radon is

conservative?

(b) What is the steady-state concentration of radon (in pCi/L) in the house if radon

decays via a first-order reaction with a rate constant of 0.025 h-1?

Explanation / Answer

(a) What is the retention time of the house?

(b) What is the steady-state concentration of radon in the house (units of pCi/L)?

Here is the system schematic Qin = 722 m3/hr Qout = 722 m3/hr Cin = 0 Cout = ? in = 250 pCi/sec

(a) The retention time () is the ratio of the volume (V) to flow rate (Q) (see section 4.1.6). V 650 m3 = 0.90 hr = = m3 Q 722 hr

(b) Start with the general form of the mass balance equation dm = min mout + mrxn dt 3

In this case there is no accumulation or reaction, so this simplifies to the following 0 = min mout + 0 min = mout where min = 0 * 722m3 / hr + 250 pCi / sec mout = C * 722(m3 / hr )(hr / 3600 sec)

Setting these equal to one another and solving for C gives C= 250 pCi / sec = 1.247 x 103 pCi/m3 = 1.25 pCi/L (722m / hr )(hr / 3600 s

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