Physics

# The Physics Philes, lesson 120: Very Specific Heat

Brrrr…it’s cold outside. Frigid, even. There’s a dusting of snow outside my window as I type. One might be forgiven for thinking that there isn’t as much heat outside as there is in the summer. But that’s not quite right, as least in the wonderful world of physics.

Temperature and heat are distinct things. Heat is an energy transfer that takes place because of a temperature difference. In physics, when we talk about heat, we are always talking about energy moving from one body or system to another. Temperature, on the other hand, is a quantitative description of how hot or cold some material is. This distinction is very important to keep in mind going forward.

Since heat is the transfer of energy, there is probably some kind of relationship between heat and other forms of energy. Guess what! There is! Sir James Joule (yeah, that Joule) did an experiment in which he found that water can be warmed by vigorously stirring it with a paddle. The paddle added energy to the water by doing work on the water, and Joule found that the rise in temperature was directly proportional to the amount of work done. We also see this same temperature change if we put the water in contact with a hotter body. It’s all about the transfer of energy.

We have a couple of different ways to refer to heat. We have the calorie (cal), which is the amount of heat required to raise the temperature of one gram of water from 14.5 ºC to 15.5 ºC. Kind of a weird definition, but it is what it is. (Also, these aren’t the same calories as we find in food, but they are related. Food calories are really kilocalories. One food calorie is actually 1000 calories.)

There is also a unit of heat that uses Fahrenheit called the British thermal unit (Btu). Like the calorie, the reference point for the Btu is the amount of heat to raise some water one degree Fahrenheit. Specifically, it’s the amount of heat required to raise the temperature of one pound of water (a weight, not a mass) from 63 ºF to 64 ºF.

These units can be useful, but neither are actual official SI units. That distinction goes to the joule, which makes sense given that heat is just a transfer of energy. Both of these unofficial units can be translated in joules. One calorie is equal to 4.186 J and one Btu is equal to 1,055 J.

OK, now let’s call a quantity of heat Q. Let’s say that Q is the quantity of heat that is required to increase the temperature of a mass m of some material from T1 to T2. It turns out that Q is approximately proportional to the temperature change, as well as the mass of the material. In addition, Q is also dependent on the nature of the material. For example, raising the temperature of water by 1 ºC takes 4190 J, which the amount of heat necessary to heat up aluminum by the same amount requires only 910 J.

As usual, math says all of this more succinctly. The heat required to change the temperature of a material with mass m can be expressed as

Q = mcΔT

Whoa, there. What is that c? This quantity is called the specific heat of a particular material. The value is different for every material.

In this equation, Q and ΔT can be positive or negative. If they are negative, that means that heat is leaving the system and the temperature decreases. If they are positive, heat is entering the system and the temperature increases.

There is more to say on this topic, but I’m afraid it will have to wait until next time.

Featured image credit: Tony Cairns via Flickr