Heat capacity

Based on the quizzes I just graded, there’s a great deal of confusion as to what specific heat capacity means.  Heat capacity does not refer to some magical, intrinsic temperature of a material–it is defined as the amount of thermal energy that is needed to raise one gram of a substance one degree Celsius.

Let’s think a little more about the equation q = m • c • ∆T.  If we take one gram of a substance, and its specific heat capacity (c) is large, that means it takes a lot of heat (q) to increase the temperature (∆T) of the material.  If the heat capacity is small, on the other hand, the same amount of heat will cause a much larger change in the temperature.  Water has a pretty large specific heat capacity, and most metals have pretty small specific heat capacities.

But what does this mean?  There’s no point in what we’re studying unless we can learn something about the natural world from it.  Building on our brief discussion of thermal equilibrium here, we can determine what the equilibrium temperature will be when two objects are brought into thermal contact.  When object 1 and object 2 reach thermal equilibrium, we can say

q1 = -q2

because the amount of heat gained by object 1 is the same amount of heat lost by object 2.  (Conservation of energy, remember?)  This tells us that we can also set

m1 • c1 • ∆T1 = -(m2 • c2 • ∆T2)

What about the special case where the two objects have the same mass?  Then we can say

m1 = m2

and we don’t even have to think about mass anymore!  We can simplify our expression to

c1 • ∆T1 = -(c2 • ∆T2)

And this is where we see that, if heat capacity c1 is large, and c2 is small, ∆T1 will be small, and ∆T2 will be large!  This is why water is so useful for cooling: water has a large specific heat capacity.

If my explanations don’t quite work for you, here’s a page with a lot of videos covering problem-solving involving specific heat capacity.  Every instructor explains things just a little differently.[1]  There are a lot of web resources for these concepts–I will post some for you, and you’re always welcome to seek out your own (but make sure the source is reliable!).  The important thing is that you find a way to learn the material that makes sense to you.

[1] When I’m lifting, two different coaches can tell me the same thing using different cues…sometimes I have no idea what one is asking me to do, but the second coach’s instruction makes perfect sense.

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