What is kinetic and potential energy?

What actually is energy? We often consider forms of energy like chemical energy, electrical energy, or thermal energy. But behind the scenes, there are only two types of energy: kinetic and potential.

Energy

If you check the units of the ideal gas law, it should be clear that both sides equal energy. In some respects, the ideal gas law is a statement about the conservation of energy.

If any of the three main variables is held constant, the other two respond predictably to keep energy of the system the same. This is also the case for the van der Waals equation and non-ideal conditions.

Types of energy

If we break down things like chemical energy, we will find that they’re a combination of these two. The chemical energy released by a chemical reaction comes from the molecules and atoms rearranging – the potential energy of the products and reactants are different, and that difference is the energy released.

In other branches of physics (notably, quantum mechanics) adding these together is known as the Hamiltonian energy (H=T+V). In thermodynamics, the combination of both of these types is known as total energy.

Kinetic energy

Kinetic energy is the amount of energy associated with motion and movement, and is defined as the energy required to accelerate an object (with mass, m) from rest to its current velocity (v).

Kinetic energy is usually written as:

[E_k=frac{:1}{2}mv^2E]

Potential energy

Potential energy is a function of configuration. It depends on relationships between objects, such as distance between two objects that attract each other.

It can also be how an object is rearranged. A good example here is a bow and arrow — when a bow is drawn back, its potential energy increases because its shape (the interaction between all the molecules that make it up) has changed. When released, that potential energy reverts back.

Other examples include gravity, where it is defined as the product of mass, acceleration due to gravity, and the distance, or height, between the two objects:

[E_p=mgh]

Calculating potential energy

This isn’t the only way to calculate potential energy. In fact, it’s one of the harder ones to calculate from base principles. As the number of possible particles increase, the number of possible interactions increase dramatically.

Potential and kinetic energy can exchange. If two objects are attracting each other, by gravity or by electrical charge, the potential energy between them can convert to kinetic energy and cause them to move closer together.

Putting energy into the particles to draw them apart, against the attractive force, adds potential energy to the system.

Temperature and energy

Temperature is an SI base unit. It is measured in Kelvin. It is the manifestation of sub-microscopic kinetic energy of particles.

These particles do not all have the same kinetic energy (so they don’t have the same speed). So temperature is a measure of the average amount of energy.

Total and internal energy

It’s important to understand the idea of a system in order to bound what we mean by energy and, importantly, energy transfer.

A system is whatever we are looking at. It doesn’t necessarily need to have a hard boundary around it, but it separates what we’re looking at from surroundings. The total energy of the system is also known as its internal energy. This means energy that is distinct from the movement of the system itself.

For example, a hot coffee cup will have an internal energy associated with the heat of the solution inside it. But this internal energy is distinct from the energy associated from picking up the cup and moving it around.

A molecule will have internal energy, but this is distinct from its movement (rotations and translations) associated with its heat. So it’s important to know where to draw the system boundary, and what can cross it.

Open systems

Open systems exchange both heat and material with the surroundings. Most real systems are technically open, because it is very difficult to completely isolate a system. There will always be leaks, and even the most efficient insulation can’t stop radiation leaving the system.

Closed systems

A closed system only exchanges heat with its surroundings. Heat is the transfer of kinetic and potential energy to the surroundings via collisions at the sub-microscopic level.

If molecules collide with a container wall, they transfer energy to it. Energy is transferred from the container wall to the molecules of the surroundings via collisions, too. Matter is not exchanged in a closed system.

Isolated system

An isolated system exchanges nothing with its surroundings. Matter cannot exchange with the surroundings, and heat does not transfer.

Truly isolated systems are effectively impossible. Heat will always transfer in some ways, but they can be approximated by many layers of efficient insulation, or by making sure the surroundings are kept at the same temperature as the system.

If this is the case, there can be no heat transferred. Any microscopic collisions that transfer energy out of the system will be balanced by microscopic collisions that transfer energy back into it.