## Heating a Room with People

I am currently sitting in a really boring meeting that is being held in a very small room. The room is packed full of people and it is hot in here. This situation reminds me of a conversation I had with an HVAC engineer years ago about the heat load that people present to a cooling system. During that discussion, the HVAC engineer casually mentioned that he models every person as a 100 W load. I should be able to estimate that number based on the average daily calorie consumption of a person. Consider the calculation I show in Equation 1.

 Eq. 1 $\displaystyle P=\frac{E}{T}=\frac{2000\text{ kcalorie}}{24\text{ hours}}\cdot \frac{1\text{ hour}}{3600\text{ seconds}}\cdot \frac{4187\text{ Joules}}{\text{kcalorie}}=96.9 \text{ W}$

where

The use of 100 W per person seems like a reasonable average number.

I am an engineer who encounters interesting math and science problems almost every day. I am not talking about BIG math here. These are everyday problems where a little bit of math really goes a long way. I thought I would write some of them down and see if others also found them interesting.
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### 2 Responses to Heating a Room with People

1. CC says:

I’ve heard the 100W figure for humans as well.

Once I was volunteering at a science day thing for kids, and the room I was helping in involved a 1W microwave transmitter and detector and a prism that would bend the microwave beam – one setup per two kids. One of the parents approached me, concerned that the microwave transmitters were heating up the room, because it was getting pretty warm in there.

• mathscinotes says:

Funny. Another example of correlation does not imply causation.

I used to volunteer at my kid’s grade school. I really enjoyed that. The only issues I ever had were with the parents – - kind of like when I coached hockey.

Mathscinotes