We all know a bunch of people in a room can make it warmer, but how much heat do 80,000 fans emit?
So people give off heat, right? But why? The law of conservation of energy states that energy, which heat is a form of, cannot be created nor destroyed. So where does our heat come from?
From food. But more specifically a word that has been unfairly demonized in popular culture: The Calorie. See the calorie is actually a measure of energy contained in food. More precisely it's the energy needed to raise 1 Kilogram of water 1 Degree celsius.
So assuming a diet of 2,000 calories a day we can calculate how much energy a human body has avaliable to emit.
We're gonna go from calories to joules per day, then to joules per hour, then joules per second.
Once we get there it's easier to visualize since a Watt is defined simply as a joule per second.
That means any given fan will give off about 97 watts per hour.
That’s like having a 100 watt light bulb in place of each one of the 80,000 fans.
But watts isn't how we usually think about heat so let's convert to BTUs per hour...doing that we come up with 26 million 447 and 94 BTUS per hour.
That means Mercedes Benz Stadium would need 734 3 ton AC chillers just to counter all that body heat!
But without an artificial cooling, we can figure out how many degrees the air in the stadium would rise. For that we gotta get into thermodynamics. Ready?
Change in temperature- delta t. Is equal to heat energy emitted divided by mass times specific heat of dry sea level air.
Plugging those numbers into the equation we get...but wait...what's the mass?
Mercedes Benz Stadium is 305 high by roughly 900 ft wide and 900 long. That gives us 247 million cubic ft. We know that dry air weights about .075 pounds per cubic foot so we get roughly 18 million lbs of air in the stadium.
Plug that in and you get an increase of 5.95 degrees an hour
Given the average Superbowl last 3 hours and 44 mins that means the temperature in the stadium, if left unchecked, would rise by 22 F by the time the confetti is flying.