# I Determine time to cool a room

1. Jul 18, 2017

### mknott

How do you calculate the time to cool down a 60'X60'X50' building filled with outside air at 96°F to 65°F with 14,250 CFM of supply air at 55°F?

2. Jul 18, 2017

### Staff: Mentor

This is a surprisingly difficult question because you have to consider the thermal mass of the building and it's contents and how efficient the airflow is. If you just want a rough estimate of how fast it can cool the air, Newton's law of cooling (or the dilution/mixing equation) can be solved numerically in a spreadsheet in about 30 seconds...

3. Jul 18, 2017

### mknott

So, what is the Newton's Law of Cooling equation and how would you solve this problem with it?

4. Jul 18, 2017

### Staff: Mentor

Is this homework or a real life situation? Either way, we like to teach here rather than spoonfeed, so you should be able to take partial answers and nudges in the right direction and move them along yourself....

With that in mind, note the late edit to my post. In this situation, Newton's Law of cooling simplifies to a dilution situation. Dilution is just a weighted average. Do you know how to calculate a weighted average?

5. Jul 18, 2017

### mknott

This is a real life project. I've looked up Newton's Law of Cooling, but what I was seeing was it doesn't take into account air flow. I'm not sure what you are talking about in how it simplifies to a dilution situation. I'm not sure how to calculate weighted average either.

6. Jul 18, 2017

### mknott

This is the equation I was looking at: T(t)=T_a + (T_o - T_a)e^(-kt)

7. Jul 18, 2017

### Staff: Mentor

A weighted average is the amount of air at one temperature plus the amount of air at another temperature divided by the total amount of air.
(V1T1+V2T2)/V3=T3

8. Jul 18, 2017

### mknott

So, how does the weighted average pertain to the equation above? I still have two variables that are unknown.

9. Jul 18, 2017

### Staff: Mentor

Just use the weighted average. You have only one unknown; the temperature after each mixing interval(T3). Do a series of 1 minute increments using that equation and you'll get your answer.

10. Jul 18, 2017

### mknott

So once I calculate all the temperatures after each interval until I reach the desired 65F, how then am I able to calculate the time to get to that temperature? Sorry if I'm not understanding you correctly.

11. Jul 18, 2017

### Staff: Mentor

Each interval is 1 minute, so you add up the number of intervals (number of calculations). The fact that the same calculation gets repeated several times is why a spreadsheet works so well...

Last edited: Jul 18, 2017
12. Jul 18, 2017

### mknott

Ok, I understand. Thank you for your help.