# Quantities and Units

In science a **Quantity** is expressed as the product of a number and a unit. A number without units often has no meaning to a scientist. A set of standard (agreed upon) units are essential not only in science, but also in commerce. The most widely accepted system of measurement in the sciences is the **International System**, otherwise known as

**S.I. Units.**

S.I. stands for Le Systéme International. This is also called the **metric system**, with which you may already be familiar.

The metric system is easy to learn and use because subdivisions and multiples of base units employ only factors of 10. Prefices indicate the size of the unit relative to a base unit.

Prefix | Symbol | Multiple of Unit |
---|---|---|

mega- | M | 1,000,000 or 10^{6} |

kilo- | k | 1,000 or 10^{3} |

deci- | d | 0.1 or 10^{-1} |

centi- | c | 0.01 or 10^{-2} |

milli- | m | 0.001 or 10^{-3} |

micro- | μ | 0.000001 or 10^{-6} |

nano- | n | 10^{-9} |

pico- | p | 10^{-12} |

The SI system defines seven base quantities, from which all other scientific quantities can be derived. These base quantities are length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity. All other quantities can be derived from these base quantities using the equations of physics and chemistry. Let's look at the base units for some base and derived quantities.

# SI Base Quantities

## Length

The SI base unit for length is the meter. The abbreviated symbol for meters is m

. A meter is slighly longer than a yard (*i.e.,* 1 m = 39.37 inches).

## Mass

The SI base unit for mass is the kilogram. The abbreviated symbol for the kilogram is kg

. 1 kg weighs approximately 2.2 pounds. The choice of the kilogram instead of the gram as the base unit for mass is only for historical reasons.

## Time

The SI base unit for time is the second. The abbreviated symbol for the second is s

.

## Electric Current

The SI base unit for electric current is the ampere. The abbreviated symbol for the ampere is A

.

## Amount of Substance

The SI base unit for amount of substance is the mole. The abbreviated symbol for the mole is mol

. We will learn more about the mole later in this course.

## Luminous Intensity

The SI base unit for luminous intensity is the candela. The abbreviated symbol for the candela is cd

.

## Thermodynamic Temperature

The SI base unit for temperature is the Kelvin. The abbreviated symbol for the Kelvin is K

. The coldest temperature theoretically possible is 0 K. You simply cannot go any lower. In fact, it is experimentally impossible to even reach 0 K.

For historical reasons it is also common to define temperature in terms of its difference from a reference temperature T_{0}=273.15 K, the freezing point of water. This is called the Celsius temperature, and the abbreviated symbol for Celsius is °C

. It is related to the Thermodynamic Temperature by the equation

T(in Celsius) = T(in Kelvin) - 273.15 K

On the Celsius scale the freezing point of water is set at 0 °C, and the boiling point is 100 °C. Thus, the coldest temperature theoretically possible is -273.15 °C.

**Warning:** Celsius and fahrenheit scales are not absolute scales and their conversion is ambiguous. Without additional information one cannot know if a value in celsius or fahrenheit should be interpreted as an absolute temperature or a temperature difference. That is, for any calculation involving ΔT you can use celsius and fahrenheit without problems, such as the heat calculated from a heat capacity and a temperature change, q = C ΔT. On the other hand, celsius and fahrenheit are not appropriate in any calculation requiring an absolute temperature, such as the ideal gas law, P V = n R T. In any case, the safest approach is to convert all temperatures into kelvin or rankines before using them in a calculation. If your final answer needs to be in celsius or fahrenheit, then perform this conversion at the end of your calculation.

To give you some other reference points:

System | Temperature |
---|---|

Sun's Interior (thermonuclear fusion of hydrogen to helium) | 10^{8} K |

Sun's Surface | 6000 K |

Earth's Core | 4600 K |

Liquid N_{2} (boiling pt.) | 77 K |

Liquid He (boiling pt.) | 4.2 K |

# Some SI Derived Quantities

## Volume

Volume is a derived quantity and has the dimensions of length^{3}. Thus, the SI unit for volume is the cubic meter which has the abbreviated symbol m

. In practice, the cubic meter is not a convenient unit for everyday use, so the cubic decimeter (dm^{3}^{3}) is used instead. Because it is so often used 1 dm^{3} is given the name **liter**. The abbreviated symbol for a liter is L

or l

.

1 liter = 1 dm^{3}

When working with even smaller volumes the cubic centimeter is more commonly used. Since

^{3}= (10 cm) (10 cm) (10 cm) = 1000 cm

^{3},

we often use 1 mL (mL is the symbol for milliliter) in place of 1 cm^{3}. You will sometimes see a mL called a cc

, which stands for cubic centimeter.

## Pressure

Pressure is a derived quantity and has the dimensions of mass/(length•time^{2}). The SI unit for pressure is kg/(m • s^{2}). This product of base units is given the name pascal

and the symbol Pa

.

1 Pa = 1 kg/(m•s^{2})

## Energy

Energy is a derived quantity and has the dimensions of mass/(length•time)^{2}. The SI unit for energy is kg/(m^{2} • s^{2}). This product of base units is given the name joule

and the symbol J

.

1 J = 1 kg/(m^{2} • s^{2})

## Electric Charge

Electric Charge is a derived quantity and has the dimensions of current•time. The SI unit for electric charge is A • s. This product of base units is given the name coulomb

and the symbol C

.

1 C = 1 A • s

## Density

Density is a derived quantity and has the dimensions of mass/length^{3}, and is defined as the mass per unit volume.

The S.I. units for density are kg/m^{3}, but these are not very convenient units for everyday use. More common units are

g/cm^{3} for solids

g/ml for liquids

g/L for gases

If we know the mass and volume of a sample, then we can calculate its density.

**A cube of lead 3.00 cm on a side has a mass of 305.0 g. What is the density of lead?**

To answer this question we need to put the mass and volume of the sample into the equation above. The mass of lead is given at 305.0 g. Although we are not given the volume directly, we do know that the sample is a cube (i.e., all sides of equal length), and that length of a side is 3.00 cm . The volume of this cube would be

^{3}= 27.0 cm

^{3}.

Thus, the density of the cube of lead is density = mass/volume = 305.0 g / 27.0 cm^{3} = 11.3 g/cm^{3}. Notice that the density is the same no matter the size or shape of the sample.