Answered

Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Discover the answers you need from a community of experts ready to help you with their knowledge and experience in various fields. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

A 90-m3 basement in a residence is found to be contaminated with radon coming from the ground through the floor drains. The concentration of radon in the room is 1.5 Bq/L under steady-state conditions. The room behaves as a CSTR and the decay of radon is a first-order reaction with a decay rate constant of 2.09 3 1026 s21 . If the source of radon is closed off and the room is vented with radon-free air at a rate of 0.14 m3 /s, how long will it take to lower the radon concentration to an acceptable level of 0.15 Bq/L

Sagot :

boffeemadrid

Answer:

25 minutes

Explanation:

V = Volume = [tex]90\ \text{m}^3[/tex]

[tex]C_0[/tex] = Radon concentration under steady state = 1.5 Bq/L

k = Radon decay rate = [tex]2.09\times 10^{-6}\ \text{s}^{-1}[/tex]

[tex]Q[/tex] = Venting rate = [tex]0.14\ \text{m}^3/\text{s}[/tex]

[tex]C_f[/tex] = Final concentration of radon = 0.15 Bq/L

Theoretical detention time is given by

[tex]\theta=\dfrac{V}{Q}\\\Rightarrow \theta=\dfrac{90}{0.14}\\\Rightarrow \theta=642.86\ \text{s}[/tex]

We have the relation

[tex]C_f=C_0e^{-(\dfrac{1}{\theta}+k)t}\\\Rightarrow t=\dfrac{\ln\dfrac{C_f}{C_0}}{-(\dfrac{1}{\theta}+k)}\\\Rightarrow t=\dfrac{\ln\dfrac{0.15}{1.5}}{-(\dfrac{1}{642.86}+2.09\times 10^{-6})}\\\Rightarrow t=1478.25\ \text{s}=\dfrac{1478.25}{60}=24.63\approx 25\text{minutes}[/tex]

The time taken to reach the acceptable level of concentration is 25 minutes.

We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.