Thermodynamics:  First Law of Thermodynamics

The term internal energy is often used synonymously with the energy of a system.  It is the sum of the kinetic and potential energies of the particles that form the system.  The last postulate in the kinetic molecular theory states that the average kinetic energy of a collection of gas particles is dependent only upon the temperature of the gas.  Since ideal gases have no potential energy, the internal energy is directly proportional to the temperature:

where R is the ideal gas constant (0.0821 L-atm/mol-K) and T is temperature (Kelvin)

If a system is more complex than an ideal gas, then the internal energy must be measured indirectly by observing any changes in the temperature of the system.  The change in the internal energy of a system is equal to the difference between the final and initial energies of the system:

The equation for the first law of thermodynamics can be rearranged to show the energy of a system in terms of the energy of its surroundings. This equation indicates that the energy lost by one must equal the energy gained by the other:

The energy of a system can change by the transfer of work and or heat between the system and its surroundings.  Any heat that is taken, given off, or lost must be complemented by an input of work to make up for the loss of heat.  Conversely, a system can be used to do any amount of work as long as there is an input of heat to make up for the work done.

This equation can be used to explain the two types of heat that can be added to a system:

  1. Heat can increase the temperature of a system.  This is sensible heat.
  2. Heat that does ONLY WORK on a system is latent heat.


The diagram above illustrates the sign (positive or negative) of the change in the energy of a system when heat and work are transferred between a system and its surroundings.


State Functions

Are the following properties state functions?

We already determined that the internal energy of a system is a state function, but work is not.  Since the change heat must complement the path that the work followed, heat cannot be a state function.
Properties that ARE state functions generally have CAPITALIZED variables.

  • e.g.  E, P, T, V, etc.

Properties that ARE NOT state functions generally have LOWER-CASE variables.

  • e.g.  q and w

Next:  "Enthalpy"