Monday, April 22, 2013

Are You a Fan of Delicious Flavors?

SHAWN: Well, Buddy, I really hope you like this. It took me 19 hours to bake. I put it in last   night before bed.
GUS: It takes 19 hours to bake a pineapple upside-down cake?
SHAWN: It does when it's being heated by a 60 W bulb.
GUS: [Looking at the cake.]  It's not upside down, Shawn.
−A scene from USA's very funny Psych 

"Psychic" detective Shawn Spencer may be a wiz at solving crimes, but does he or does he not know how to bake a pineapple upside-down cake? I've heard it both ways. How much heat (i.e. thermal energy) would a pineapple upside-down cake cooked with an Easy Bake Oven absorb over 19 hours?

An Easy Bake Oven might hold 100 grams of cake. According to Paula Deen, a pineapple upside-down cake should be placed in an oven preheated to 350°F (~180°C). This is an increase of about 160°C from room temperature. In order to increase the cake's temperature like this, you need to add some energy.

Not enough butter for Ms. Deen's tastes

According to Shawn, the Easy Bake light bulb operates at 60 Watts.  Only a fraction of this power goes into actually heating the cake, while the rest heats the air, metal, plastic, and other materials that make up the Easy Bake Oven. Assuming only 10 percent of the power goes into actual productive heating of the cake, over 19 hours the cake would absorb 400,000 Jules of energy.1
Easy Bake Oven...the real slow cooker

Since 400,000 Jules of energy isn't a particularly enlightening figure, let's see if we can put it another way. How much would the cake's temperature rise with this much energy? For a given amount of energy, the change in an object's temperature can be determined by its heat capacity.2 I suspect no one's ever measured the heat capacity of a pineapple upside-down cake. That said, pineapple upside-down cake is, like most food, made largely of water. As such, its heat capacity should be similar to water's. That would put it around 4.2 J/g·°C.3 With this heat capacity, a 100 gram cake heated with 400,000 Jules of energy would have its temperature increase to about 1300°F. Note that this assumes all the thermal energy absorbed by the cake stays in the cake. In actuality, as the cake gets hotter it will start losing some of its thermal energy to the cooler air outside the Easy Bake.

This was a fun calculation. The only way it could have been better, is if someone did an actual experiment involving an Easy Bake Oven and a pineapple upside-down cake. Wait a minute...what's this? Someone doing an actual experiment involving an Easy Bake Oven and a pineapple upside-down cake and kicking ass with science? Come on, know that's right!

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.

[1] Yes, I am aware that "Jules" is actually spelled "Joules", but somehow, I suspect Shawn Spencer would prefer it this way.  On a related note, Shules really needs to get back together pronto.  Seriously, we've all had a crappy week.  It'd be awesome to get some good news for a change.
[2] An object's heat capacity measures an object's "capacity" for storing heat.
[3] According to at least one reference, bread has a heat capacity between 1.65 and 2.73 J/g·°C.  Another reference lists pineapples as having a heat capacity between 1.72 to 3.68 J/g·°C, so we're at least in the ballpark.

No comments:

Post a Comment