The worst high school physics question EVER

Here is a multiple choice question from an online high school physics question.  It’s bad, but it’s probably not actually the worst ever.

It goes something like this:

You have three objects that start at the same temperature.  Which one cools off the fastest?

  1. A dry bean
  2. Toast
  3. Water

What is your answer and why is this bad?

I’ll be honest, I answered this question incorrectly – well, I should say that my answer didn’t agree with the key.  Let’s go over the options.

Water

I’m starting with water because this is the answer I chose.  Why would water cool off the fastest?  My assumption was that the water would evaporate and cool off the liquid more than the other two objects.

Of course the evaporative cool depends on several things:

  • The water temperature
  • The air temperature and humdity
  • The volume of water
  • The surface area of water.

If I take some water and pour it into a very shallow pan with a large surface area, this stuff is going to cool off quick.  Note: here is an older post about evaporative cooling.

This answer was wrong.

Toast

This was my second answer.  What is special about toast and why would they choose it?  In my mind, toast is special because it has lots of holes.  Lots of holes means that it has a large surface area to volume ratio.

Since things radiate thermal energy through the surface area, things with high surface area to volume ratios cool off faster.  This is why small objects cool off faster than large objects.  This is also why the moon’s core is cooler than the Earth’s core (the moon is smaller).

Oh, this is also how a heat sink works.  Large surface area to volume ratio.

This answer was wrong.

Dry Bean

A dry bean could cool off the fastest because it is small (high surface area to volume ratio) and it is low density.  I assume if it has a low density it has a low specific heat capacity.  This means that with a low specific heat capacity, the dry bean has a small amount of thermal energy even though it has the same temperature as the water and the toast.

This is essentially the same reason that you can put pizza on aluminum foil in the oven.  Once it is hot, you can touch the aluminum foil, but not the pizza.  Although they are at the same temperature, the aluminum foil has less thermal energy to burn you (because of the low mass).

This was the correct answer (according to the people that wrote this dumb question).

Writing questions isn’t so simple

I think what the author really wanted to ask was “which has the lowest thermal energy?”  But even then, you have to take mass and specific heat capacity into consideration.

It’s really just a super bad question.  Super bad.  Oh, but it’s probably not the worst one.  I saw some others that were just as bad if not worse, but I have blocked them from my memory.

Heat. It’s a four letter word

Heat. You have heard it before. You have used it. I have even used it. Do we need this word? No. Is this a useful word? No.

Let me start with the definition as usually stated in a physics type text: (this is from [dictionary.com](http://dictionary.reference.com/browse/heat))

*heat:* a nonmechanical energy transfer with reference to a temperature difference between a system and its surroundings or between two parts of the same system.
This definition is fine. It is not wrong, but is it needed? Not really. Couldn’t we just say energy transfer? Actually, I like to use this in the following equation:
![work energy](http://blog.dotphys.net/wp-content/uploads/2008/08/work-energy.jpg)
In this equation (the work-energy equation) W stands for the work, and Q is typically referred to as “heat”. This equation is used for systems of particles, if you just have one particle, then the fundamental equation is:
![work](http://blog.dotphys.net/wp-content/uploads/2008/08/work.jpg)
So, expanding to macroscopic systems, Q is still work. Work is the only way to change the energy of a system. I like to call Q (like some textbooks do) as micro-work. Q is the work done on the system due to particle collisions from another object.

The other non-sciencey definitions are clearly wrong. The common usage of the word heat is also clearly abused. This can be seen in phrases like “add heat” or “remove heat”. Another poor usage (which I have used) is “heat this thing up” which implies heat is a verb.

Ok, then if we do not use heat – what then? I think if you want to talk about transfer of energy, say transfer of energy. If you want to use Q, call it microwork. If you want to talk about the energy something has because it is hot, say thermal energy.