## The First Law of Thermodynamics

**First Law of Thermodynamics:** The conservation of energy - energy into a closed system must equal energy out of a closed system. Energy cannot be created or destroyed, but can be changed and transferred.

**Definition of Work**

Work is defined as a force acting in the direction of some displacement, generally represented as into or out of a system or subsystem. It can be represented on a pressure-volume diagram of a change in state as the area under the curve between an initial volume and a final volume as well as an initial pressure and final pressure.

Mathematically, work can be represented as:

Where:

W = work

F = force

dx is the displacement

The integral is from state 1 to state 2

If you consider a system, work done to the system is considered positive work (adding energy to the system) and work done by the system is considered negative work (removing energy from the system).

**Definition of Heat**

Heat is defined simply as a form of energy that is transferred between the boundary of one system to the boundary of another system in the direction of lower temperature. Temperature has been defined and standardized based on easily repeatable points of reference and gives a basic understanding of how to quantify the change of heat between systems.

Heat is transferred at the boundary of a system. For example, consider a gas at a high temperature and a gas at a low temperature separated by a boundary. The molecules in the high temperature gas will collide with the boundary, transferring kinetic and/or internal energy to the molecules making up the boundary and hence slowing down the gas molecule (lowering the energy and temperature). When a molecule in the low temperature gas collides with the boundary, it will be hit by a molecule with more energy and will be rebounded faster, therefore transferring energy to the lower temperature molecule (raising the energy and temperature). Because heat is considered a transient property, it is only transferred between two systems of different temperature. If the systems are at the same temperature, they would be considered at steady state or equilibrium with each other in terms of temperature.

If you consider a system, heat transferred into the system is considered positive heat transfer (adding energy to the system) and heat transferred out of the system is considered negative (removing energy from the system).

**Understanding Total Energy**

The total energy represents all energy contained by a system in the current state. In thermodynamics, the energy in a system is most easily interpreted by three extensive properties – physical property of a system that is additive for subsystems – that define the total energy:

The internal energy of a system includes energy contained by the system per unit mass that is not considered kinetic or potential energy. The kinetic and potential energies are determined based on the frame of reference of the control system.

If we consider a closed system changing from one state (arbitrary state 1) to another state (arbitrary state 2), the total energy equation can be written:

Where U is the internal energy.

If the equation is integrated between state 1 and state 2, the change in total energy can be written as:

Where (subscript 1 is variable at state 1, subscript 2 is variable at state 2):

E = total energy

U = internal energy

m = mass

V = velocity

g = constant gravity value

Z = position

**The First Law of Thermodynamics**

The total energy equation can be used to define the energy contained by a closed system. The first law of thermodynamics generally states that energy can be changed and transferred but cannot be created or destroyed. In the case of thermodynamics, it has been observed that energy is transferred into and out of (through the boundaries of) a closed system through the form of work and heat.

Therefore, the first law indicates there must be conservation of energy – energy into a closed system must equal energy out of a closed system. Mathematically, this looks like:

Or, the change in total energy in a closed system is equal to the heat added to the system (or -Q if heat is removed) plus the work done to the system (or -W if work is done by the system).

To simplify, assume the closed system is in a state of thermodynamic equilibrium and there is no change in kinetic or potential energy. Therefore, the only change in energy in the system is the internal energy:

*Jarrett Linowes**Mechanical Engineeromniamfg@gmail.com*

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