Energy is everywhere and it comes in many different forms. Its most common forms are internal, kinetic, potential, mechanical, and electrical. Let's take a look at a few types below.
Internal energy is the molecular activity of a substance. You can think of this as vibration, translation, and rotation. Internal energy is proportional to temperature and it is heavily associated with the phase of the substance. Remember back to chemistry when we learned about latent energy, or the additional energy needed for phases changes.
Now the sum of the vibration, translation, and rotation energy with the latent energy is equal to the thermal energy of a substance, and this is approximately equal to the internal energy excluding chemical or nuclear reactions. Internal energy is one of many different types of energy we will take in account for our analysis. Speaking of which, let's move onto the next!
Kinetic energy is the energy associated with group motion of a substance relative to a reference frame. Kinetic energy is often written in terms of its approximation
[ 1 ]
$$ KE = \frac{1}{2} m v^2 $$
Energy has the units of Joules ($ J $) which can be broken down into $ N•m $, or Newton meters. Now it will be common throughout this guide when I refer to specific kinetic energy. This is very similar to Eq. (1) in that it is the kinetic energy divided by the mass such that we get
[ 2 ]
$$ ke = \frac{1}{2} v^2 $$
and the units for specific kinetic energy is in Joules per kg, or $ \frac{J}{kg} $. This concept can be very beneficial to use during analysis because we can solve problems without direct knowledge of "how much" mass there is. After all, remember that energy is an extensive property, which means it is dependent on mass. However, if we use specific energy instead, it would be an intensive property instead because it is not dependent on mass, it is independent.
Potential energy is elevation energy in a gravitational field. As an object is brought to a higher altitude, it has more potential energy due to the gravitational attraction of the Earth. Objects that fall from higher heights have an impact speed of higher velocities, considering the same amount of drag; this is due to there being more potential energy to transfer into kinetic energy by the time of impact.
Potential energy can be written as
[ 3 ]
$$ PE = m g z $$
and similarly to kinetic energy, potential energy can be written as specific potential energy.
[ 4 ]
$$ pe = g z $$
Both Eqs. (3-4) have the same units as Eqs. (1-2), respectively.
Now that we have talked about internal, kinetic, and potential energy, we can start to put it all together. The total energy in a system can then be written as a sum of the three energies.
[ 5 ]
$$ E = U + KE + PE $$
And the total specific energy can be written as
[ 6 ]
$$ e = u + ke + pe $$
For fixed, closed systems, the system's change in energy will be solely due to the change in internal energy. This is because $ KE = PE = 0 $, hence leaving $ \Delta E = \Delta U $. Now let's pretend we have a moving fluid going through a frictionless pipe. We know the mass flowing into the pipe will equal the mass flowing out of the pipe. This is because the system is steady-state. We can connect this mass flow rate with the density of the fluid, its velocity, and the area of the tube.
[ 7 ]
$$ \dot{m} = \rho v A $$
The mass flow rate equation is incredibly useful and may be familiar from Introduction to Aerospace. $ \dot{m} $ can also be related to total specific energy and the energy change rate.
[ 8 ]
$$ \dot{E} = \dot{m} e $$
One last thing I want to mention is energy quality. This is the ability for the energy to be converted to work without loss. Kinetic energy and potential energy have very good qualities compared to thermal energy. This is because thermal energy is much more difficult to direct compared to the other types of energy. It dissipates in every direction from its source; that is why insulation is often used for trying to stop thermal energy loss.
It should also be noted that thermal energy can only move when there is a pressure difference, and for systems where there is no heat transfer across the boundary, these are called adiabatic systems.