In this first post, I will introduce several fundamental concepts that are important for understanding the world. These concepts include energy, work, power, current, voltage, resistance, entropy, velocity, efficiency, and derivatives. By adopting a first principles perspective, I can simplify my understanding of the world by reducing everything to these concepts. These concepts and their corresponding equations form the building blocks for natural physical laws such as the Law of Conservation of Energy, Ohm's Law, and the Laws of Thermodynamics, and Newton's Laws, which govern our reality. In this post, I will explain each concepts, provide the relevant equations, and demonstrate how they are related. I will also delve deeper into each concept and the associated laws in future posts.
ENERGY is the ability to do work or cause change (measured in Joules). It can take many forms, such as electrical energy, kinetic energy, potential energy, thermal energy, nuclear energy, or sound energy. In my opinion, energy is at the core of everything. However, for now, I will just explain some of the equations. Since I am an electrical engineer, I will mostly focus on electrical energy, but please note that energy can take many forms and I will touch upon all forms throughout the blog.
Kinetic Energy = 1/2 x Mass x Velocity^2
Thermal Energy = mass x heat capacity x change in temperature solid = mass x specific heat liquid
Potential Energy = mass x gravity x height
Electrical Energy = Power x Time
POWER is the rate with respect to time at which work is done; it is the time derivative of work (measured in Watts = Joules per second).
Power = dW / dt where “d = Derivative, W = Work, t = Time”
Kinetic Power = P(t) = Force x Velocity = (Mass x Acceleration) x (Velocity)
Electrical Power = P(t) = I(t) x V(t) where “I = Current, V = Voltage, t = Time” (Ohms Law)
CURRENT is a measure of the flow of electrical charge in a circuit or wire (measured in amps). Think of it as the amount of water flowing through a pipe at any given time. It is a key factor in determining the behavior of electrical devices and systems.
Current = Voltage / Resistance (Ohms Law)
VOLTAGE is a measure of the potential difference between two points in an electrical circuit (measured in volts). It can be thought of as the "pressure" that drives the flow of electrical current in a circuit. Imagine two reservoirs of water connected by a pipe. If both reservoirs have the same amount of water, the potential difference and pressure, or voltage, is zero. However, if one has more water than the other, water will flow with pressure from the reservoir with more water to the one with less water until the potential difference is depleted and the water no longer flows.
Voltage = Current x Resistance (Ohms Law)
RESISTANCE is the measure of how much a system opposes the flow of electrical current ( measured in ohms). When current flows through a circuit, it encounters resistance, which causes some of the energy in the current to be dissipated as heat. Insulating materials, like rubber and glass, have high resistance and do not conduct electricity well. Insulators create resistance that restricts the flow of electrical current. Resistance is an important factor in the energy balance of an electrical circuit, as it determines how much energy is dissipated as heat and how much is available to perform useful work.
Resistance = Voltage / Current (Ohms Law)
WORK Is the transfer of Energy from one system to another through the application of force over a distance (measure in joules). It’s an important in energy physics because it allows us to analyze the transfer of energy in various systems and determine how energy is being converted from one form to another. This is useful in a wide range of applications, from analyzing the energy efficiency of machines to understanding the behavior of gases and the transfer of heat.
Work = Force x Distance
Force = Mass x Acceleration
The equation for force is given by Newton's Second Law of Motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
ENTROPY is the measure of disorder or randomness in a given system. The Greek root of the word translates to "a turning towards transformation", with transformation meaning chaos. As humans, we tend to prefer to minimize and control chaos to restore order to our systems. We can only achieve that by applying energy and work to the system. However, entropy is one thing that will always win, no matter how much energy and work we apply.
Entropy = Boltzmann constant x ln(# of configurations or states)
VELOCITY is a measure of an object's speed and direction of motion (measured in units of distance per time -mph-). The definition for velocity in an economy is the rate at which people exchange money. I am writing both definitions because this is a science and money blog. Velocity is an important concept in many areas of physics, including classical mechanics, electromagnetism, and relativity.
Velocity = Distance / Time
EFFICIENCY is a measure of how much useful work or output is produced compared to the amount of energy or input required for a process or system. In an energy system, efficiency affects how much of the available energy is being used effectively. If a system has more resistance, it will have lower efficiency. If it has more power, it will have higher efficiency. Since our world and lives are governed by 24 hours in a day, we must find ways to create more efficient systems.
Efficiency = (Useful Work / Energy Input) x 100% Useful work refers to the work that is performed by a system or process that is actually useful, rather than waste energy or heat that is produced as a byproduct of the process.
DERIVATIVE is the "instantaneous" rate of change of one quantity with respect to another in time. It helps us understand how things change over time and can be used to predict future events. Geometrically, derivatives are the slope of a curve at a particular point on the curve. An example of a derivative is power, which is the time derivative of work. Another example is velocity, which is a derivative of acceleration. The derivative of acceleration is momentum. These can be thought of as first, second, and third order effects.
f'(x) = [f(x+h) - f(x)] / h where f'(x) is the derivative of the function f(x) at the point x, and h is a small value used to approximate the derivative.
Example is the derivative of the function f(x) = x^2 would be represented as: f'(x) = 2x
Now that we have covered the basics that I base most of my life off of its time to set sail with PirateWaves.
With Love, CookieMonster