## Wednesday, May 8, 2013

### Fire in a Bottle

Here's a fun physics demonstration where you get to burn stuff.  Just place some cotton in a syringe and press down quickly.

Voila!  Instant ignition. How hot does it get inside a fire syringe?

Let's assume you push down with 10 pounds (~44 newtons) of force over a distance of 10 centimeters.  While pushing you do work on the gas inside.  Work is equal to force times distance:

work = (44 newtons) × (10 cm) = 4.4 J.

A syringe with 0.25 cm2 cross-sectional area and a 20 cm length will contain roughly 5 milligrams of air. The heat capacity for the air in the container is about 1.0 J/g·K. From these numbers we can find the temperature of the air will rise by 9000 kelvin, giving a final temperature of 15,000 degrees Fahrenheit! For reference, the cigarette lighter burns at about 3000 degrees Fahrenheit, so the syringe is clearly hot enough to set the cotton on fire!

Aaron Santos is a physicist and author of the books How Many Licks? Or How to Estimate Damn Near Anything and Ballparking: Practical Math for Impractical Sports Questions. Follow him on Twitter at @aarontsantos.