Air containing 0.04% carbon dioxide is pumped into a room whose volume is 6000 ft3. The air is pumped in at a rate of 2000 ft3/min, and the circulated air is then pumped out at the same rate. If there is an initial concentration of 0.2% carbon dioxide, determine the subsequent amount in the room at any time.

Here is the full question:

Air containing 0.04% carbon dioxide is pumped into a room whose volume is 6000 ft3. The air is pumped in at a rate of 2000 ft3/min, and the circulated air is then pumped out at the same rate. If there is an initial concentration of 0.2% carbon dioxide, determine the subsequent amount in the room at any time.

What is the concentration at 10 minutes? (Round your answer to three decimal places.

0.046 %

Explanation:

The rate-in;

= 0.8

The rate-out

=

=

We can say that:

where;

A(0)= 0.2% × 6000

A(0)= 0.002 × 6000

A(0)= 12

Integration of the above linear equation =

so we have:

∴

Since A(0) = 12

Then;

Hence;

∴ the concentration at 10 minutes is ;

=  %

= 0.0456667 %

= 0.046% to three decimal places