There are many forms that energy can take. Some of these forms are thermal, mechanical, kinetic, potential, electric, magnetic, chemical, and nuclear. When you sum all of the forms of energy acting within a system you will obtain the systems total energy.

Now in thermodynamics you don’t need to know what the total energy is within a system. The reason why is because thermodynamic only considers the change in total energy. This means you can set the total energy to zero at some convenient reference point when analyzing the change in energy in a thermodynamics problem.

There are two types of energy that make up the energy of a system. They are macroscopic energy and microscopic energy. Macroscopic energy is energy that passes through boundary layer of the system and reacts to the environment or another system. Microscopic energy however is the energy at a molecular level within in the system. Microscopic energy can be considered as the systems internal energy.

**Internal Energy**

As mentioned in earlier sections internal energy represents the microscopic energy within a system. Internal energy is represented by the letter U. The internal energy is basically the sum of different types of microscopic energies, such as the, sensible energy, latent energy, chemical energy, and nuclear energy.

Sensible energy is the kinetic energy of the particles within the system. This includes both rotational kinetic energy, and transverse kinetic energy. Latent energy on the other hand is the associated energy that determines that phase of the system. In other words a certain amount of internal energy is required for the system to have solid phase, a liquid phase, or a gas phase. The chemical energy is the measurement of the energy between the atomic bonds of the molecule. Finally, nuclear energy is the amount of energy of associated to the nuclear bonds of an atoms nucleus.

**Kinetic Energy**

Kinetic energy is the energy of a system that relates the mass of a system to the velocity of a system. There are two types of kinetic energy that need to be considered. They are transverse kinetic energy and rotational kinetic energy. Transverse kinetic energy is represented by equation 1, while rotational kinetic energy is represented by equation 2.

**(Eq 1) ** $Ke = \frac{1}{2}mv^2$

$m$ = mass

$v$ = velocity

**(Eq 2) ** $Ke =\frac{1}{2}Iω^2$

$I$ = MAss Moment of Inertia

$ω$ = angular Velocity

**Potential Energy**

Potential energy represents the stored energy within a system. An example of potential energy is when a system is held at a certain height there is a stored amount of energy within that system which will be released when the system is allowed to fall. This can be calculated using equation 3.

**(Eq 3) ** $Pe=mgz$

$m$ = mass

$g$ = gravitational constant 9.81 $\frac{m}{s^2}$ or 32.2 $\frac{ft}{s^2}$

$z$ = height

**Total Energy**

As mentioned earlier total energy is the sum of all of the energies acting on and within the system. So that would mean the total energy of a system if the internal energy, kinetic energy, and potential energy of the system was known would be represent by equation 4.

**(Eq 4) ** $E=U+Ke+Pe$

$U$ = Internal Energy

$Ke$ = Kinetic Energy

$Pe$ = Potential Energy

In some cases the total energy would be represented as total energy per unit mass; equation 5.

**(Eq 5) ** $e=\frac{U+Ke+Pe}{m}$

Now if a closed system was stationary that would mean that the kinetic energy and potential energy of the system would be zero. So any changes in energy would be a direct result of changes of the internal energy changing within the system. This type of system is known as a stationary system.

**Control Volumes**

Unlike closed systems, control volumes can have fluid flowing through them. This is an additional energy that needs to be considered. To consider the energy of the fluid stream you would need to know what the mass flow rate of the fluid is. To calculate the mass flow rate you would use equation 6.

**(Eq 6) ** $\dot{m}=ρAv$

$ρ$ = density

$A$ = cross-sectional area

$v$ = velocity

Once you know what the mass flow rate you can calculate the energy of the fluid stream over time. In other words you are calculating the power of the fluid stream. Refer to equation 7.

**(Eq 7)** $\dot{E}=\dot{m}e$

**Mechanical Energy**

Mechanical energy is a form of energy that can be converted into mechanical work. An example of mechanical energy is the energy of steam that is used to move the turbines within a power plant. Both kinetic energy and potential energy are forms of mechanical energy. Also, even though pressure itself is not a form of energy, the forces of pressure acting on a fluid can produce mechanical work. To calculate mechanical energy per unit mass refers to the equation below. Equation 8 is a form of Bernoulli’s equation.

**(Eq 8) ** $e_{mech}=\frac{P}{ρ}+\frac{v^2}{2}+gz$

$P$ = Pressure

$ρ$ = Density

$v$ = velocity

$g$ = gravitational constant

$z$ = fluid head

To calculate the power in relation to mechanical energy equation 9 would be used.

**(Eq 9) ** $\dot{E}_{mech} = \dot{m}e_{mech}$