# Conservation of Energy: Closed System

The 1st Law of Thermodynamics states that the total change in energy, E, for a closed system is equal to the difference between the heat added to the system and the work done by the system.

Mathematically the 1st Law of Thermodynamics can be written as

Note that sign convention for heat transfer and work requires that the negative sign be used on the right hand side of this equation.

The time rate of change of the 1st Law of Thermodynamics is given by the equation

where the dot over a variable indicates the time derivative of the variable.

The total energy in the system includes the internal energy, U, the kinetic energy, KE, associated with the motion of the system, and the potential energy, PE, associated with the position of the system relative to a some reference. The 1st Law of Thermodynamics for a closed system can then be written as

## Learning Objectives:

Learn definition of 1st Law of Thermodynamics, Learn difference between and open and closed system, learn notation used for heat and work