# Hints for in-class problem #4

This one seems to be giving a lot of people trouble, so I thought I’d try to clear up some misconceptions.

• This post contains some helpful information, since we can assume the coffee is in thermal equilibrium with the gallium spoon as the spoon melts.  The final temperature for the spoon will be the same as the final temperature for the coffee.  You’re going to be solving for the mass of the coffee, since you know the mass of the spoon, and you have the initial and final temperatures (convert to ºC!) and heat capacities for the spoon and the coffee.
• I said you’d be solving for the mass of the coffee, but the problem asks for the volume of coffee.  What property (that’s stated in the problem!) helps you convert mass to volume?
• I gave you the heat capacity of water/coffee as 4.184 J/(g•K), but I failed to explain that this is equivalent to 4.184 J/(g•ºC)!  This works because the “spacing” between ºC and K is the same: there are 100 degrees between the freezing point of water and the boiling point of water in both scales.  (Convert for yourself if you don’t believe me!)
• We’re looking for the minimum amount of coffee needed to melt the spoon, and the answer is so small it might surprise you a little.

I believe in you, and you can all get this one.  I wouldn’t put something this tricky on an exam, but you can definitely expect at least one heat capacity problem.  The hardest problems we solve are going to be the in-class sets.  This is useful because you all get to learn how to collaborate to find the solution, and you get to check your understanding by discussing with your classmates!  I know some of you are a little confused and terrified of looking stupid in front of others (I was one of you, years ago), and that makes these exercises painful and unpopular.  This is why I’m bribing you with candy.  Showing someone else your thought processes is really useful if you’re doing science for a living, or if you’re teaching, or if you’re trying to ace a technical job interview.

Please comment if there’s anything else that isn’t clear!  (Or future candy suggestions.)

By the way, the gallium spoons do exist.  Here’s one in action!

Bonus: what kind of mixture do the water and molten gallium form?