# Specific Heat Calculation

Here’s a block of copper. Doesn’t look like it, but it’s the best I could do. For now, let’s pretend that it has a mass of 0.1kg and is at a temperature of 1000C (which we ensure by dunking it for a while in some boiling water.) It isn’t but we’ll get to that later. In the meantime, we get some water, say 200g or 0.2kg in a polystyrene beaker (so we don’t have to worry about it receiving any heat) and take the temperature. Let’s say it’s room temperature, 20oC which we can measure with a thermometer on the bench.

We drop the copper in the water and stir it gently. Looks easy, but it isn’t in practice. Probably the best way is to tie some cotton to the block and pretend it’s a teabag when we transfer it. The copper gives its heat to the water. After a short while, we take the temperature of the water again.

Heat lost by copper = heat gained by water

mass of copper x SHC of copper x temperature fall of copper = mass of water x SHC of water x temperature rise of water

We know that the SHC of water = 4200J/kgoC – look it up in a book.

Let the final temperature be 23oC

Temp fall of copper = 100-23 = 77oC

Temp rise of water  = 23-20 = 3oC

So, 0.1 x SHCcopper x 77 = 0.2 x 4200 x 3

Solving gives us SHC for copper = 327 J/kgoC

The actual value is close to 400 J/kgoC. Our measurement is too low. Why is this? Here’s a question. Is the copper at exactly 100oC  when it goes into the water? If not, what might its actual temperature be? Suppose its actual temperature is close to 90oC, because it loses some heat by convection and radiation on the way over. So the temperature of the copper falls by only 67oC, giving us a value of 376 J/kgoC, which is a little bit better.

Here’s the trick. Heat is always lost on transfer so measured SHC’s are always too low.