Photovoltaics: Energy

Before we look into the physical principles of photovoltaics, let's define some basic connections between the three very important physical quantities: energy, force and power. These connections are taken from classical mechanics, but are generally valid. The learning objectives for this post are to understand how force, energy and power are related. We will learn to define and relate different types of energy. Finally, we will look at the first and second law of thermodynamics and discuss what their implications are for solar cells. We will start with the force.

The force can be defined as any influence on an object that changes its motion. A force is exerted as a result of an interaction between two or more objects. The objects can be in physical contact, or at a distance, like gravitational forces or magnetic forces. Imagine a very strong man exerting a force on a granite block. The force causes the block to accelerate. According to Newton’s second law, the acceleration ‘a’ depends on the magnitude of the exerted force ‘F’ and the mass ‘m’ of the object that undergoes the acceleration. We can gather from that that the force and acceleration are vectors, or directional quantities. The units of force are kilogram times meter per second squared, which is known as a newton, denoted by ‘N’. The amount of energy used in this interaction is given by the product of the force and the distance ‘s’.

Energy is a very useful concept to evaluate an amount of effort to accomplish a system change, or to put it simply, the ability of a system to do work. Let's put this definition of energy in practice. Now, imagine a tomato. We lift the tomato up to a height of 1 meter, for which we have to overcome the gravitational force ’G’. Since the required amount of energy is equal to the force times the distance, it is equal to ‘G’ times the height ‘h’. The gravitational force near the surface of the earth, is equal to the mass of the tomato times the gravitational acceleration, which is denoted by the lowercase ‘g’. The amount of energy required to lift the tomato is therefore equal to 1 kilogram times meter squared per second squared.

This is known as a joule, after the English physicist James Prescott Joule. Since energy is equal to a force applied over a certain distance, 1 joule can also be defined as the amount of energy required to apply a force of 1 Newton over a distance of 1 meter. We just defined energy as the ability to exert a force over a certain distance. But that is not the only definition of energy. Energy can be converted from one form to another and all these manifestations of energy that we can observe are related through the great physical constants that define our universe.

We have related energy to the mass of an object and the height of that object, with respect to the surface of the earth, through the gravitational acceleration, which is derived from the gravitational constant. According to Einstein’s famous equation, energy and mass are also interchangeable, through the speed of light in vacuo, denoted by c-naught. The energy contained in a voltage, which is a difference in electric potential charge, is related through the elementary charge, denoted by ‘q’. The elementary charge is the charge of a single proton or electron, which have similar charge but of opposite sign. The elementary charge is expressed in Coulomb, after the French physicist Charles-Augustin de Coulomb, which is equal to an ampere times a second. The amount of thermal energy present in a temperature is defined using Boltzmann’s constant, denoted by ‘k-B’.

Finally, the discrete particles of energy contained in an electromagnetic radiation, like light, is a function of only its frequency, denoted by 'nu'. Energy and frequency are related though Planck’s constant, denoted by 'h'. All these constants, and implicitly all these definitions of energy, play an important role in the field of photovoltaics. Now, on to power. The power ‘P’ is defined as the amount of energy used per unit time, denoted by ‘t’. Power is therefore expressed in joules per second. 1 Joule per second is also known as a Watt, after Scottish engineer James Watt. As an example, with 70 joules of energy we could power this 70 Watt incandescent light for exactly one second.  We could also power this 7 Watt LED light for 10 seconds, or 10 of these LED lights for 1

second.

Joules are not the only unit used to express a certain amount of energy. 1 joule is a very small amount compared to the human energy consumption. Therefore a different unit of energy is used for the production and consumption of electrical energy, namely the kiloWatt-hour. 1 kiloWatt-hour, as the name implies, is the amount of energy consumed if a power of 1 kiloWatt is applied for one hour. Since 1 kiloWatt is equal to 1000 joules per second, and there are 3600 seconds in an hour, 1 kiloWatt-hour is equal to 3.6 megajoules. The amounts of energy used in the atomic physics relevant for solar cells, on the other hand, are very small. We therefore use the unit electronvolts. An electronvolt is the amount of energy a body with a charge of one elementary charge gains or loses when it is moved across the electric potential difference of 1 volt. 1 electronvolt is therefore equal to the elementary charge times 1 volt, which equals 1.6 times 10 to the power of minus 19 joules. 

For the large scale production and consumption of energy, a unit is used that is much larger than the joule, namely the ton of oil equivalent, or toe. A toe is defined as the amount of energy released by the burning of 1 ton of crude oil. 1 toe is equal to 4.2 times 10 to the power 10 joules. Finally, in the food industry the unit of calorie is used. 1 calorie is defined as the amount of energy required to raise the temperature of 1 gram of water by 1 degree Celsius, at a pressure of 1 atmosphere. One calorie equals to 4.2 joules. We discussed how energy can be converted from one form into another form. Practical examples are wind turbines that convert the kinetic energy, contained in the

particle flow that we know as the wind, into mechanical energy, which is then converted

into electrical energy.

Chemical energy stored in fossil fuels are converted into thermal energy, which is in turn converted into mechanical energy and finally electrical energy. Solar cells convert the energy contained in electromagnetic radiation directly in electrical energy. The first law of thermodynamics tells us that throughout all of these conversions, in a closed system, the total amount of energy is conserved. This means that, in a closed system like the universe, the total amount of energy does not change.  The second law of thermodynamics, however, states that the entropy of a system can only ever increase or stay the same. So, what exactly is the entropy of a system? The entropy is a measure of amount of dispersion of matter and energy in a closed system. The fact that entropy only increases, implies that the amount of dispersion will only ever increase. This is illustrated by the figure on the right. 

We can see a closed system, with a large blue area containing a liquid at a low temperature, and a small red area containing a liquid at a high temperature. The two areas are thermally separated by a membrane. We know from experience that when we remove the membrane, the hot liquid will diffuse into the cold liquid, producing a mix with a temperature somewhere in between. Where first the hot molecules were contained in a small area, they now have dispersed throughout the system and the entropy has increased. Since the hot liquid could more easily be converted into other forms of energy, the quality of the energy contained in the closed system has decreased. The entropy can therefore also be interpreted as a measure of the usefulness of a type of energy.

The lower the entropy of a type of energy, the easier it is to convert that energy into another type, so the higher its usefulness. Mechanical and electrical energy are very useful, since they can be converted into one another with an efficiency of over 90%. Both can be converted into thermal without any loss.Thermal energy, however, can not be converted into electrical energy directly, and its conversion into mechanical energy occurs at an efficiency of under 60%. Thermal energy is the most distributed, and least useful form of energy. Furthermore, the usefulness of thermal energy, and its conversion efficiency into other forms of energy, decreases strongly with its temperature. For any natural energy conversion or even every natural process, the quantity of energy will remain the same. The quality of the energy will decrease. This has some implications for photovoltaics as well. When an electric current, which is flow of charge carriers, moves through an object its usefulness will decrease. 

During this flow some power is dissipated as thermal energy. The amount of dissipated heat is equal to the current squared times the resistance of the material. 1 Joule of thermal energy is therefore dissipated when an electric current of 1 ampere passes through a resistance of 1 ohm for 1 second.

In summary, we defined the force as any influence on an object that changes its motion and the energy as ability to apply a force over a certain distance. The power we defined as the energy exerted per unit time. We introduced a number of alternative definitions of which the kiloWatt hour and electronvolt are of special interest to us as solar cell engineers. We discussed how one form of energy can be converted into another, without changing the total amount of energy in a closed system. Then we found that even though the quantity of the energy in a system does not change, the quality of the energy will only ever decrease or stay the same. Thermal energy is the most dispersed, and least useful form of energy and we discussed the thermal energy dissipation in a material.

Source: https://www.amazon.com/Solar-Energy-engineering-photovoltaic-technologies-ebook/dp/B0198VHPHM/ref=sr_1_1?qid=1551542806&refinements=p_27%3AArno+Smets&s=digital-text&sr=1-1