Working content >MacroModels>Heat and temperature>Heat capacity

            It is possible for an object to absorb heat and raise its temperature.   Because objects are made of different materials, the amount of heat required will vary depending on how hard it is to get the molecules to increase their motion and hence their temperature.  For a given material, the amount of heat required to raise 1 kg of that material by one degree is called the specific heat, c.   The units of c will therefore be energy per mass per degree (K).  So in our typical SI units this would be J / kg K.  Because a particular object has a particular mass, we can calculate the amount of heat necessary to raise that object’s temperature by one degree (K).  This is the objects heat capacity, C, and is simply the specific heat of the material times the object’s mass.

                                        (1)

Therefore, the units of heat capacity, C, are kg * J/kg K which simplifies to J/K.  This makes sense as it is the amount of energy (heat) that is needed for each degree K that the temperature is raised.

            We can use heat capacity to figure out how much energy is needed to increase an object’s temperature by 1 K.  An example would be the amount of energy that your body uses to raise your temperature by 1 K, say when you have a slight fever.  If there is no heat loss (an assumption we will come back to later) then the heat needed to make the temperature increase by 1 K is

                                        (2)

where Q is the amount of heat in J, and ΔT is the temperature change (in this case 1 K).  For a 150 lb person (68.2 kg), we can assume that the heat capacity of a person is the same as water, 1006 J/kg K.  So the heat needed is

It’s hard to get a feel for joules.  One way is to think about how this energy is to compare it to that coming from a 100 W light bulb.  This amount of energy is equivalent to the energy emitted over 685.9 seconds (or about 11.4 minutes) from that bulb.  That seems reasonable for raising your body temperature by 1 K.