Deflation of Frosty

This morning I was walking to the library from my apartment downtown and I saw the inflatable snowman and Santa Claus that had been set up earlier this week in front of Theta Chi.  But, sadly, both of the characters were partially deflated.  This morning was particularly cold, and that made me think about the relationship between temperature and volume of an ideal gas.  Using Charles' Law, we determined that temperature and volume are directly proportional for ideal gases.  This is due to the fact that the gas particles at lower temperatures have less energy and are moving more slowly.  This means that there are fewer collisions between the gas particles and the sides of the inflatable characters.  So, I figured that the deflation was a result of the drop in temperature that the inflatable characters were subjected to since they were initially blown up.  I guessed that the temperature on that day was about 45℉, or 280°K, and the temperature when I walked by today was 30℉, or 272°K.  In order to find the initial volume of the snowman, I treated it as a cylinder with a height of 8 ft and a radius of 2 ft.  Using V=𝝅r^2h, I found that the volume was 100.5 ft^3, or 2846 L.  I was then able to find the change in volume using Charles' law.

 V1/T1=V2/T2.

V2= V1T2/T1

V2= (2846 L)(272°K)/(280°K)

V2= 2765 L

ΔV= 81 L

(81 L/ 2846L)(100) = 3%

This change in temperature led to a 3% drop in the volume of the inflatable snowman.  When I walked back this morning, the snowman looked like it had experienced more than a 3% drop in volume, which means there must be some other factors in play.  But, I thought this example of how temperature affects the volume of an object filled with an ideal gas was very relevant to our recent discussions in class.