Internal Energy, Heat, and Specific Heat


Energy comes to us in various forms: kinetic and potential energies of various types. Consider a system (e.g. gas in a cylinder). If the system as a whole is moving then we say the system has kinetic energy. But if we pin the system down and donít allow it to move as a whole, there is still kinetic energy present due to the random motion of the atoms of the system. In addition, these atoms might exert forces on each other and therefore, there could be internal potential energies associated with these "bonds". Of course, for an ideal gas there are no bonds.

The internal energy of a system is defined as the total of the random internal kinetic energies of the atoms and the total internal potential energies due to the bonds between atoms.

Internal energy is not a new concept or form of energy. On the other hand, heat is a new concept that is central to thermodynamics. Heat is an energy TRANSFER process. Heating occurs when two objects, having different temperatures, exchange energy due only to the difference in temperatures.

This notion of heat is called the mechanical model of heat and it became the dominant view in the mid-1800ís following the famous Joule mechanical equivalent of heat experiment. Before Joule people believed heat to be an invisible, weightless fluid that flowed between two objects that have a different temperature. The fluid was called caloric, therefore, this was called the caloric model of heat.


The thermal properties of an object or material are an important trait. One of the most important thermal properties is found when an amount of energy, Q, is delivered to the object by heating. Generally, Q causes the temperature of the object to change by DT. If for a given DT, Q has to be large, we say the object can "hold a lot of heat" and therefore, it has a large heat capacity, C, where

C º Q/DT.

C is a property of an object, it will depend on the composition of the object as well as the mass of the object. For the same material, C will get bigger if you have more mass of the material.

A related term called specific heat, c, depends only on the material of the object and not on the mass of the object,

c º Q/mDT.

Values of c have been measured and appear in a table in your text.

Rearranging we have,

Q = mcDT.

APPLICATION: Calorimetry

In calorimetry we mix together two substances that start with different temperatures and wait till thermal equilibrium is achieved at a final temperature, Tf. Measuring the mass of each constitutent and all of these temperatures allows one to find the specific heat of one of the constituents provided you know the specific heat of the other constituent.

The fundamental principle used is energy conservation, which takes the guise

|Qgained by one constituent| = |Qloss by the other constituent|




EXAMPLES [in class]