Base Units in SI Help

The Kelvin

The SI unit of temperature is the kelvin, symbolized K (uppercase and nonitalicized). It is a measure of how much heat exists relative to absolute zero, which represents the absence of all heat and which is therefore the coldest possible temperature. A temperature of 0 K represents absolute zero. Formally, the kelvin is defined as a temperature increment (an increase or decrease) of 0.003661 part of the thermodynamic temperature of the triple point of pure water. Pure water at sea level freezes (or melts) at + 273.15 K and boils (or condenses) at + 373.15 K.

What, you might ask, is the meaning of triple point? In the case of water, it’s almost exactly the same as the freezing point. For water, it is the temperature and pressure at which it can exist as vapor, liquid, and ice in equilibrium. For practical purposes, you can think of it as freezing.

The Ampere

The ampere, symbolized by the uppercase nonitalicized English letter A (or abbreviated as amp), is the unit of electric current. A flow of approximately 6.241506 × 10 ¹⁸ electrons per second past a given fixed point in an electrical conductor produces an electrical current of 1 A.

Various units smaller than the ampere are often employed to measure or define current. A milliampere (mA) is one-thousandth of an ampere, or a flow of 6.241506 × 10 ¹⁵ electrons per second past a given fixed point. A microampere (μA) is one-millionth or 10 ⁻⁶ of an ampere, or a flow of 6.241506 × 10 ¹² electrons per second. A nanoampere (nA) is 10 ⁻⁹ of an ampere; it is the smallest unit of electric current you are likely to hear about or use. It represents a flow of 6.241506 × 10 ⁹ electrons per second past a given fixed point.

The formal definition of the ampere is highly theoretical: 1A is the amount of constant charge-carrier flow through two straight, parallel, infinitely thin, perfectly conducting media placed 1 m apart in a vacuum that results in a force between the conductors of 2 × 10 ⁻⁷ newton per linear meter. There are two problems with this definition. First, we haven’t defined the term newton yet; second, this definition asks you to imagine some theoretically ideal objects that cannot exist in the real world. Nevertheless, there you have it: the physicist venturing into the mathematician’s back yard again. It has been said that mathematicians and physicists can’t live with each other and they can’t live without each other.

The Candela

The candela, symbolized by the lowercase nonitalicized pair of English letters cd, is the unit of luminous intensity. It is equivalent to 1/683 of a watt of radiant energy emitted at a frequency of 5.4 × 10 ¹⁴ hertz (cycles per second) in a solid angle of one steradian. (The steradian will be defined shortly.) This is a sentence full of arcane terms! However, there is a simpler, albeit crude, definition: 1 cd is roughly the amount of light emitted by an ordinary candle.

Another definition, more precise than the candle reference, does not rely on the use of derived units, a practice to which purists legitimately can object. According to this definition, 1 cd represents the radiation from a surface area of 1.667 × 10 ⁻⁶ square meter of a perfectly radiating object called a blackbody at the solidification temperature of pure platinum.

The Mole

The mole, symbolized or abbreviated by the lowercase nonitalicized English letters mol, is the standard unit of material quantity. It is also known as Avogadro’s number and is a huge number, approximately 6.022169 × 10 ²³ . This is the number of atoms in precisely 0.012 kg of carbon-12, the most common isotope of elemental carbon with six protons and six neutrons in the nucleus.

The mole arises naturally in the physical world, especially in chemistry. It is one of those strange numbers for which nature seems to have reserved a special place. Otherwise, scientists surely would have chosen a round number such as 1,000, or maybe even 12 (one dozen).

A Note About Symbology

Up to this point we’ve been rigorous about mentioning that symbols and abbreviations consist of lowercase or uppercase nonitalicized letters or strings of letters. This is important because if this distinction is not made, especially relating to the use of italics, the symbols or abbreviations for physical units can be confused with the constants, variables, or coefficients that appear in equations. When a letter is italicized, it almost always represents a constant, a variable, or a coefficient. When it is nonitalicized, it often represents a physical unit. A good example is s, which represents second, versus s , which is often used to represent linear dimension or displacement.

From now on we won’t belabor this issue every time a unit symbol or abbreviation comes up. But don’t forget it. Like the business about significant figures, this seemingly trivial thing can matter a lot!

Practice problems of these concepts can be found at: Units And Constants Practice Test