Thermal Energy

When talking about thermodynamics there are several key terms that are often misused.


Heat is actually the flow of thermal energy from one object to another.  Objects do not contain heat. We use the letter Q to represent the flow of heat or heat transfer. Later, we will define the amount of heat used to warm an object up with the equation


where m is the mass of the object, c is the specific heat capacity, and T is the temperature.  As heat is a flow of energy, we should use Joules as the unit, although you might also commonly see calories or British Thermal Units as units for heat.

Internal Energy

When we talk about the word heat, we usually mean the Internal Energy of an object.  Temperature is related to the average kinetic energy per particle.  If we were to add up all of the kinetic energies and potential energies for the particles, then we would have the Internal Energy.  When talking about an ideal gas, we often assume there is no potential energy, and only consider the kinetic energy of the particles.  For an ideal gas, we can write that the Internal Energy U, is

U = (3/2)NkT

where N is the number of molecules, k is Boltzmann’s constant, and T is the temperature in the Kelvin scale.  By this model, we can say that a body a zero Kelvin has no internal energy, and thus no motion.  Of course, we are ignoring potential energy and assuming an ideal gas.  And the hotter the gas, the more energy.  But remember, the total energy also depends on the number of molecules


Work is an important related concept in thermodynamics. Earlier, you have defined work as

W= F·d

However, when dealing with gasses, you have played with Pressure and Volume.  We can also define work as

W = P·V

If you define P = F/A and V = A·d, then you find these statements are equivalent.

Some of you may have noticed that when you vigorously pumped the syringe that some strange things happened.  You are doing WORK on a system when you compress it.  Thus you are giving the system thermal energy!  Of course, if it is in equilibrium with the environment, then it will cool down.