Derran Tyler
Inactive Member
SI Units (fundamental)
Length: m (metre)
Mass: kg (kilogram)
Time: s (second)
Electrical Current: A (ampere)
Thermodynamic Temperature: K (kelvin)
Amount of matter: mol (mole)
SI Units (derived)
Area m²
Volume m³
Frequency Hz (hertz, 1/s)
Density kg/m³
Speed, Velocity v (m/s)
Angular Velocity v (rad/s)
Acceleration a (m/s²)
Angular Acceleration a (rad/s²)
Force N (newton, kg·m/s²)
Pressure Pa (pascal, N/m²)
Work, Energy J (joule, N·m)
Power W (watt, N·m/s)
Specific Heat Capacity cp (J/(kg·K))
Thermal Conductivity k (W/(m·K))
Electrical potential difference V (volt, W/A)
Magnetic flux Wb (weber, V·s)
Magnetic flux density T (tesla, Wb/m²)
Unified Atomic Mass Unit u (1.660565E-27 kg)
Electron-volt eV (1.602E-19 J)
SI Prefixes
Y (Yotta) 10^21
E (exa) 10^18
P (peta) 10^15
T (tera) 10^12
G (giga) 10^9
M (mega) 10^6
k (kilo) 10^3
iso 10^0
m (milli) 10^-3
m (micro) 10^-6
n (nano) 10^-9
p (pico) 10^-12
f (femto) 10^-15
a (atto) 10^-18
y (yocto) 10^-21
Physics Constants:
Speed of light in vacuum c = 3E8 m/s
Electron rest mass me = 5.49E-4 u
Neutron rest mass mn = 1.0087 u
Proton rest mass mp = 1.0072 u
Hydrogen atom rest mass m1H = 1.0078 u
Deuterium atom rest mass m2H = 2.0141 u
Carbon atom rest mass m1C = 12.0000 u (exact; 1u is defined as 1/12 the mass of Carbon-12)
Universal gas constant R = 8.31 K/mol·K
Avogadro constant NA = 6.02E23 atoms/mol
Stefan-Boltzmann constant s = 5.67E-8 W/(m²·K4)
Gravitational constant G = 6.6726E-11 m³/(s²·kg)
Bohr radius rB (hydrogen atom radius) = 5.29E-11 m
Proton radius = 1.2E-15 m
Proton magnetic moment mp = 1.41E-26 J/T
Light-year = 9.46E15 m
Planck constant = 6.626E-34 J·s
Mass Density
White dwarf star core ~ 1010 kg/m³
Uranium nucleus ~ 3·1017 kg/m³
Neutron star core ~ 1017 to 1018 kg/m³
Black hole ~ 1019 kg/m³
Energy Density (at 100% efficiency)
Matter/antimatter annihilation = 9E16 J/kg
Deuterium fusion = 6.2E14 J/kg
Uranium-235 fission = 8.9E13 J/kg
Hydrogen burning = 1.2E8 J/kg
Methane gas burning = 5.0E7 J/kg
Coal burning ~ 2.3E7 J/kg (depending on grade of coal)
TNT detonation = 4.2E6 J/kg
Power Intensities:
Power intensity at surface of Sun ~ 6E7 W/m²
Power intensity of oxy-acetylene torch ~ 1E7 W/m²
Power intensity of largest modern lasers built to date ~ 1E19 W/m²
Temperatures
Laboratory or fusion reactor plasma = 5E7 K
Shock wave in atmosphere at Mach 20 = 2.5E4 K
Luminous nebulae = 1E4 K
Freezing temperature of water (0°C) = 273.15 K
Specific Heats
Aluminum = 960 J/kg·K
Carbon (graphite) = 710 J/kg·K
Iron = 420 J/kg·K
Air = 994 J/kg·K
Hydrogen = 14200 J/kg·K
Pure water = 4180 J/kg·K
Miscellaneous:
Energy required to ionize hydrogen = 13.58 eV/atom (1.3 GJ/kg)
Energy required to split deuterium nuclei into neutrons and protons = 2.2 MeV/atom (105 TJ/kg)
Astronomical Constants and Errata
The Milky Way Galaxy
Mass ~ 2.2E41 kg
Radius ~ 50,000 light years
Number of stars ~ 100 billion
Density of interstellar space ~ 1E-18 to 1E-21 kg/m³
The Sun (Sol)
Radius = 6.96E8 m
Mass = 1.989E30 kg
Surface temp = 5800 K
Surface temp = 3800 K in sunspots
Core density = 1.6E5 kg/m³
Core temp = 15.6 million K
Corona temp ~ 1 million K
Power output = 3.827E26 W
Orbital radius around the centre of the galaxy ~ 3E20 m
Upper/Lower Limits
There appears to be considerable confusion about the meaning of upper and lower limits.
An upper limit is a figure for the absolute highest possible value of a given figure (ie- the figure cannot possibly be higher than this limit, but it can be much lower).
A lower limit is a figure for the absolute lowest theoretically possible value of a given figure.
Efficiency
The laws of physics, particularly the Second Law of Thermodynamics, prevent any process from ever being perfect. Nothing is 100% efficient anywhere in the universe. Nothing can be measured or controlled to 100% exact precision. No process can occur in zero elapsed time. These concepts are simple, easily understood, and obvious to any scientifically trained person. However, since most people lack scientific training and more importantly, they lack the scientific mindset, they seem unable to grasp these simple concepts. Some people's "analyses" of their technology invariably include phrases like "perfect targeting", "instant reaction", "100% efficiency", etc. even though any such assumptions inevitably lead to highly unrealistic upper limits rather than reasonable estimates.
Force, Energy, and Power
The concepts of force, energy, and power are fundamental building blocks of science. No one can claim to have even a remote familiarity with science unless he or she has a firm grasp on these concepts- anyone without a firm grasp on these concepts cannot understand the more complex scientific principles.
Force: the Physics definition of Force (as opposed to the various unscientific colloquial definitions of force or The Force) is defined in Webster's New World Dictionary as "the cause, or agent, that puts an object at rest into motion or alters the motion of a moving object." That's probably as good as definition as any - a fundamental concept like force is difficult to define accurately without resorting to equations or circular definitions involving synonyms. In equation format, F=ma as implied by Newton's Second Law of Motion. In other words, the amount of force required to accelerate an object is proportional to the rate of acceleration multiplied by the mass of the object.
Energy
Definition: Energy is perhaps the most fundamental concept in science. All events and processes can be analyzed strictly in terms of energy balances, from obvious examples like power plants, drive motors, and refridgeration systems to less obvious examples like the biological processes in the human body and the severity of collisions. Energy balances can be used to determine whether a process is possible at all, and the extent to which a process is reversible. Energy can take many forms - mechanical, kinetic, electrical, thermal, electromagnetic, chemical, entropic, etc. A full description of all the various types of energies and the various methods by which they can be related to various situations and processes is obviously beyond the scope of this document. However, we can say that the units of energy have the dimensions of force multiplied by distance, although there are many other ways to combine units to result in energy.
The First Law of Thermodynamics: This law is the most fundamental concept of physics: it states that the total amount of energy in a closed system is constant. A more popular way of describing it is to say that energy can neither be created or destroyed, but I personally prefer the former definition. The meaning is the same in either case, but it is important to remind people of the importance of the closed system in energy analyses.
Energy Balances: Basically, energy balances involve "before and after" states of energy. An example is a 10kg block of steel resting on the ground compared to the same block suspended 10m above the ground. The suspended block has ~981J more potential energy than the block sitting on the ground, so at least 981J of energy will be required to go from one state to the other. The height change cannot be accomplished without adding 981J of energy (in some form or other) into the system because that would mean that some of its new potential energy came "out of nowhere", a clear violation of the First Law of Thermodynamics. If far more energy is poured into the system (say, 2kJ), then the excess energy must go somewhere- the block has only gained 981J of potential energy, so the extra 1019J must become something else, eg. thermal energy in the steel or the surrounding air. Note: it is perfectly possible to expend energy without adding energy to your intended target: if you push against a concrete wall with all of your might, you will expend large quantities of chemical energy within your body without adding any significant energy to the wall. This is not a violation of energy balances or the First Law of Thermodynamics- you expended energy in your body, but you never added any energy to the wall. In the overall scheme of things, chemical energy was transformed into thermal energy in your body but no mechanical energy was added to the system.
Power: Power is the rate at which energy is expended. A knowledge of both power and energy output is required to determine the destructive power of a weapon, because a small amount of energy can be released at a very high rate, thus resulting in a large power output, or a large amount of energy can be released at a very low rate, thus resulting in a low power output. In either case, the destructive capabilities of the weapon would be far lower than a high-power, high-energy weapon. A high-power, low-energy weapon will simply not be able to do a lot of work on its target, so the power level is only impressive from a mathematical standpoint. A low-power high-energy weapon may be able to perform a lot of work on its target, but if the power level is extremely low then various energy-dissipation mechanisms will come into play, preventing the energy from concentrating in a single location to the point where it can be dangerous.
Newton's Laws of Motion
Inertia: "Every body persists in its state of rest or of uniform motion in a straight line unless it is compelled to change that state by forces imposed on it."
Force and acceleration: "The rate of change of momentum of a body is proportional to the resultant force acting on the body and is in the direction of that force." This law is often expressed as the resultant equation, F=ma.
Action/reaction: "To every action there is always opposed an equal reaction; or, the mutual attractions of two bodies upon each other are always equal, and directed to contrary parts." This concept is very poorly understood by a large number of people. Let's suppose your mass is 70kg. As you sit in your chair under 1g conditions reading this page, you are therefore exerting roughly 690N of force upon the chair. The direct implication of Newton's third law is that the chair is exerting 690N of force back up against your posterior. Similarly, when an aircraft moves through the atmosphere at constant speed, its engines push it forward with (for example) 250kN of force. The aerodynamic drag of the aircraft must push back with the same force.
Philosophy
The philosophy of science is a subject for much discussion and a real discussion is beyond the scope of this document. However, the basic philosophy of science is that it exists to describe the physical universe. The key word is "describe." It does not exist to promulgate belief systems, support or deny any particular set of beliefs, or create technology. Its profound impact on society and technology is a side-effect, not its intended purpose.
The basic scientific method is quite simple: analyze measured data, formulate theories which fit the data, and then perform experiments designed to disprove the theories. If those experiments fail to disprove those theories, the theories gain weight. Notice here the important distinction between failing to disprove a theory and proving the theory. It is impossible to prove a scientific theory.
Suppose we have numerous theories which we have failed to disprove, and which fit the facts. How do we choose between them? We use Occam's Razor, which states that when faced with numerous theories that all fit the facts, the simplest theory will always be the correct one. This may sound like an arbitrary decision, but it is not: this is the way the universe works. Without Occam's Razor, we could potentially generate an infinite number of theories, of progressively increasing complexity, to explain any given phenomenon.
Length: m (metre)
Mass: kg (kilogram)
Time: s (second)
Electrical Current: A (ampere)
Thermodynamic Temperature: K (kelvin)
Amount of matter: mol (mole)
SI Units (derived)
Area m²
Volume m³
Frequency Hz (hertz, 1/s)
Density kg/m³
Speed, Velocity v (m/s)
Angular Velocity v (rad/s)
Acceleration a (m/s²)
Angular Acceleration a (rad/s²)
Force N (newton, kg·m/s²)
Pressure Pa (pascal, N/m²)
Work, Energy J (joule, N·m)
Power W (watt, N·m/s)
Specific Heat Capacity cp (J/(kg·K))
Thermal Conductivity k (W/(m·K))
Electrical potential difference V (volt, W/A)
Magnetic flux Wb (weber, V·s)
Magnetic flux density T (tesla, Wb/m²)
Unified Atomic Mass Unit u (1.660565E-27 kg)
Electron-volt eV (1.602E-19 J)
SI Prefixes
Y (Yotta) 10^21
E (exa) 10^18
P (peta) 10^15
T (tera) 10^12
G (giga) 10^9
M (mega) 10^6
k (kilo) 10^3
iso 10^0
m (milli) 10^-3
m (micro) 10^-6
n (nano) 10^-9
p (pico) 10^-12
f (femto) 10^-15
a (atto) 10^-18
y (yocto) 10^-21
Physics Constants:
Speed of light in vacuum c = 3E8 m/s
Electron rest mass me = 5.49E-4 u
Neutron rest mass mn = 1.0087 u
Proton rest mass mp = 1.0072 u
Hydrogen atom rest mass m1H = 1.0078 u
Deuterium atom rest mass m2H = 2.0141 u
Carbon atom rest mass m1C = 12.0000 u (exact; 1u is defined as 1/12 the mass of Carbon-12)
Universal gas constant R = 8.31 K/mol·K
Avogadro constant NA = 6.02E23 atoms/mol
Stefan-Boltzmann constant s = 5.67E-8 W/(m²·K4)
Gravitational constant G = 6.6726E-11 m³/(s²·kg)
Bohr radius rB (hydrogen atom radius) = 5.29E-11 m
Proton radius = 1.2E-15 m
Proton magnetic moment mp = 1.41E-26 J/T
Light-year = 9.46E15 m
Planck constant = 6.626E-34 J·s
Mass Density
White dwarf star core ~ 1010 kg/m³
Uranium nucleus ~ 3·1017 kg/m³
Neutron star core ~ 1017 to 1018 kg/m³
Black hole ~ 1019 kg/m³
Energy Density (at 100% efficiency)
Matter/antimatter annihilation = 9E16 J/kg
Deuterium fusion = 6.2E14 J/kg
Uranium-235 fission = 8.9E13 J/kg
Hydrogen burning = 1.2E8 J/kg
Methane gas burning = 5.0E7 J/kg
Coal burning ~ 2.3E7 J/kg (depending on grade of coal)
TNT detonation = 4.2E6 J/kg
Power Intensities:
Power intensity at surface of Sun ~ 6E7 W/m²
Power intensity of oxy-acetylene torch ~ 1E7 W/m²
Power intensity of largest modern lasers built to date ~ 1E19 W/m²
Temperatures
Laboratory or fusion reactor plasma = 5E7 K
Shock wave in atmosphere at Mach 20 = 2.5E4 K
Luminous nebulae = 1E4 K
Freezing temperature of water (0°C) = 273.15 K
Specific Heats
Aluminum = 960 J/kg·K
Carbon (graphite) = 710 J/kg·K
Iron = 420 J/kg·K
Air = 994 J/kg·K
Hydrogen = 14200 J/kg·K
Pure water = 4180 J/kg·K
Miscellaneous:
Energy required to ionize hydrogen = 13.58 eV/atom (1.3 GJ/kg)
Energy required to split deuterium nuclei into neutrons and protons = 2.2 MeV/atom (105 TJ/kg)
Astronomical Constants and Errata
The Milky Way Galaxy
Mass ~ 2.2E41 kg
Radius ~ 50,000 light years
Number of stars ~ 100 billion
Density of interstellar space ~ 1E-18 to 1E-21 kg/m³
The Sun (Sol)
Radius = 6.96E8 m
Mass = 1.989E30 kg
Surface temp = 5800 K
Surface temp = 3800 K in sunspots
Core density = 1.6E5 kg/m³
Core temp = 15.6 million K
Corona temp ~ 1 million K
Power output = 3.827E26 W
Orbital radius around the centre of the galaxy ~ 3E20 m
Upper/Lower Limits
There appears to be considerable confusion about the meaning of upper and lower limits.
An upper limit is a figure for the absolute highest possible value of a given figure (ie- the figure cannot possibly be higher than this limit, but it can be much lower).
A lower limit is a figure for the absolute lowest theoretically possible value of a given figure.
Efficiency
The laws of physics, particularly the Second Law of Thermodynamics, prevent any process from ever being perfect. Nothing is 100% efficient anywhere in the universe. Nothing can be measured or controlled to 100% exact precision. No process can occur in zero elapsed time. These concepts are simple, easily understood, and obvious to any scientifically trained person. However, since most people lack scientific training and more importantly, they lack the scientific mindset, they seem unable to grasp these simple concepts. Some people's "analyses" of their technology invariably include phrases like "perfect targeting", "instant reaction", "100% efficiency", etc. even though any such assumptions inevitably lead to highly unrealistic upper limits rather than reasonable estimates.
Force, Energy, and Power
The concepts of force, energy, and power are fundamental building blocks of science. No one can claim to have even a remote familiarity with science unless he or she has a firm grasp on these concepts- anyone without a firm grasp on these concepts cannot understand the more complex scientific principles.
Force: the Physics definition of Force (as opposed to the various unscientific colloquial definitions of force or The Force) is defined in Webster's New World Dictionary as "the cause, or agent, that puts an object at rest into motion or alters the motion of a moving object." That's probably as good as definition as any - a fundamental concept like force is difficult to define accurately without resorting to equations or circular definitions involving synonyms. In equation format, F=ma as implied by Newton's Second Law of Motion. In other words, the amount of force required to accelerate an object is proportional to the rate of acceleration multiplied by the mass of the object.
Energy
Definition: Energy is perhaps the most fundamental concept in science. All events and processes can be analyzed strictly in terms of energy balances, from obvious examples like power plants, drive motors, and refridgeration systems to less obvious examples like the biological processes in the human body and the severity of collisions. Energy balances can be used to determine whether a process is possible at all, and the extent to which a process is reversible. Energy can take many forms - mechanical, kinetic, electrical, thermal, electromagnetic, chemical, entropic, etc. A full description of all the various types of energies and the various methods by which they can be related to various situations and processes is obviously beyond the scope of this document. However, we can say that the units of energy have the dimensions of force multiplied by distance, although there are many other ways to combine units to result in energy.
The First Law of Thermodynamics: This law is the most fundamental concept of physics: it states that the total amount of energy in a closed system is constant. A more popular way of describing it is to say that energy can neither be created or destroyed, but I personally prefer the former definition. The meaning is the same in either case, but it is important to remind people of the importance of the closed system in energy analyses.
Energy Balances: Basically, energy balances involve "before and after" states of energy. An example is a 10kg block of steel resting on the ground compared to the same block suspended 10m above the ground. The suspended block has ~981J more potential energy than the block sitting on the ground, so at least 981J of energy will be required to go from one state to the other. The height change cannot be accomplished without adding 981J of energy (in some form or other) into the system because that would mean that some of its new potential energy came "out of nowhere", a clear violation of the First Law of Thermodynamics. If far more energy is poured into the system (say, 2kJ), then the excess energy must go somewhere- the block has only gained 981J of potential energy, so the extra 1019J must become something else, eg. thermal energy in the steel or the surrounding air. Note: it is perfectly possible to expend energy without adding energy to your intended target: if you push against a concrete wall with all of your might, you will expend large quantities of chemical energy within your body without adding any significant energy to the wall. This is not a violation of energy balances or the First Law of Thermodynamics- you expended energy in your body, but you never added any energy to the wall. In the overall scheme of things, chemical energy was transformed into thermal energy in your body but no mechanical energy was added to the system.
Power: Power is the rate at which energy is expended. A knowledge of both power and energy output is required to determine the destructive power of a weapon, because a small amount of energy can be released at a very high rate, thus resulting in a large power output, or a large amount of energy can be released at a very low rate, thus resulting in a low power output. In either case, the destructive capabilities of the weapon would be far lower than a high-power, high-energy weapon. A high-power, low-energy weapon will simply not be able to do a lot of work on its target, so the power level is only impressive from a mathematical standpoint. A low-power high-energy weapon may be able to perform a lot of work on its target, but if the power level is extremely low then various energy-dissipation mechanisms will come into play, preventing the energy from concentrating in a single location to the point where it can be dangerous.
Newton's Laws of Motion
Inertia: "Every body persists in its state of rest or of uniform motion in a straight line unless it is compelled to change that state by forces imposed on it."
Force and acceleration: "The rate of change of momentum of a body is proportional to the resultant force acting on the body and is in the direction of that force." This law is often expressed as the resultant equation, F=ma.
Action/reaction: "To every action there is always opposed an equal reaction; or, the mutual attractions of two bodies upon each other are always equal, and directed to contrary parts." This concept is very poorly understood by a large number of people. Let's suppose your mass is 70kg. As you sit in your chair under 1g conditions reading this page, you are therefore exerting roughly 690N of force upon the chair. The direct implication of Newton's third law is that the chair is exerting 690N of force back up against your posterior. Similarly, when an aircraft moves through the atmosphere at constant speed, its engines push it forward with (for example) 250kN of force. The aerodynamic drag of the aircraft must push back with the same force.
Philosophy
The philosophy of science is a subject for much discussion and a real discussion is beyond the scope of this document. However, the basic philosophy of science is that it exists to describe the physical universe. The key word is "describe." It does not exist to promulgate belief systems, support or deny any particular set of beliefs, or create technology. Its profound impact on society and technology is a side-effect, not its intended purpose.
The basic scientific method is quite simple: analyze measured data, formulate theories which fit the data, and then perform experiments designed to disprove the theories. If those experiments fail to disprove those theories, the theories gain weight. Notice here the important distinction between failing to disprove a theory and proving the theory. It is impossible to prove a scientific theory.
Suppose we have numerous theories which we have failed to disprove, and which fit the facts. How do we choose between them? We use Occam's Razor, which states that when faced with numerous theories that all fit the facts, the simplest theory will always be the correct one. This may sound like an arbitrary decision, but it is not: this is the way the universe works. Without Occam's Razor, we could potentially generate an infinite number of theories, of progressively increasing complexity, to explain any given phenomenon.
