Temperature Scales and Measurements

2.5 Temperature Scales

  • Definition and Calibration of Thermometers

    • Thermometers are calibrated to assign numerical values to temperatures.
    • A temperature scale is defined using two fixed points, based on reproducible physical phenomena.
    • Commonly chosen points:
    • Water freezes—0°C (At Standard Atmospheric Pressure)
    • Water boils—100°C (At Standard Atmospheric Pressure)

  • Standard Temperature Scales in the U.S.

    • Three scales in common use:
    • Fahrenheit
    • Celsius
    • Kelvin
    • Fahrenheit is primarily used in the U.S. and is not often used in laboratories.

  • Fahrenheit Temperature Scale

    • Invented by Daniel Gabriel Fahrenheit (AD 1686-1736).
    • Also credited with inventing the mercury-in-glass thermometer.
    • Scale details:
    • Freezing point of water: 32°F
    • Boiling point of water: 212°F
    • The range between freezing and boiling is divided into 180 equal increments (degrees).

  • Celsius Temperature Scale

    • Formerly called Centigrade, named after Anders Celsius (AD 1701-1744).
    • Scale details:
    • Freezing point of water: 0°C
    • Boiling point of water: 100°C
    • Initial definition had 0°C as boiling point and 100°C as freezing point, which was reversed later.
    • Conversion relation:
    • Size of Celsius degree unit is almost double that of Fahrenheit:
      • (1°C = 1.8°F)
    • Used in laboratories, while both scales are common for general use in the U.S.

  • Absolute Temperature Scales

    • Significance of Absolute Zero:
    • Theoretical lowest possible temperature:
      • Calculated as -273°C
      • Also calculated as -459°F
    • Kelvin Temperature Scale:
    • Uses absolute zero as its zero point.
    • No negative values because absolute zero is the lowest limit.
    • Named after Lord Kelvin (William Thomson, AD 1824-1907).
    • Units are called Kelvins, not degrees.
    • 0 K corresponds to absolute zero, with units equivalent in size to Celsius degrees.

36 | Essential Laboratory Mathematics

  • General Considerations for Measurements

    • Ensure all units of measure are identical before performing calculations.
    • Many times requires conversion of one unit to another.

  • Example Calculation:

    • Given:
    • (16.5 ext{ mL})(0.25 ext{ L})/1.5 ext{ mL}
    • Desired unit is mL; therefore, convert units before solving.
    • Convert 0.25 ext{ L} to mL:
      • 0.25 ext{ L} = 250 ext{ mL} (move decimal three places to the right).
    • Substitute converted values:
    • (16.5 ext{ mL})(250 ext{ mL})/1.5 ext{ mL} = 2750 ext{ mL}
    • Round to the appropriate number of significant figures (2 significant figures due to minimum accuracy in factors):
    • Final answer: 2800 mL.

  • Practice Problem Set 2.4

    • Convert units as indicated for various problems (numerical conversions of measurements provided).

Decimal Bumping

  • Understanding Metric Prefixes:

    • SI metric prefixes are based on powers of 10.
    • To convert a unit involves adjusting the number based on its position relative to the metric prefixes.
    • Moving right reduces the unit size (dividing into smaller units).
    • Moving left increases unit size (multiplying into larger units).

  • Examples of Decimal Moves:

    • 4.29 kg to g:
    • Move three places right:
      • 4.29 ext{ kg} = 4290 ext{ g}.
    • 15 mL to L:
    • Move three places left:
      • 15 ext{ mL} = 0.015 ext{ L}.

  • Notable Prefix Transfers:

    • Movement between certain prefixes (like milli- to micro-) represents a change of 10^{3} and must be considered when moving between units.

  • Conversion Factors:

    • Useful method for changing measurement units: Multiply the original unit by a conversion factor from tables.
    • A conversion factor is the ratio of a quantity in one unit to that in another.
    • Example:
      • 1 L = 1000 mL
      • Use conversion factor rac{1000 ext{ mL}}{1 ext{ L}} to convert units, allowing cancellation of unwanted units.
    • Conversion Examples:
    • Convert 0.015 ext{ L} to mL:
      • 0.015 ext{ L}( rac{1000 ext{ mL}}{1 ext{ L}} ) = 15 ext{ mL}.
    • Convert 250,000 ext{ m} to kilometers:
      • (250,000 m)( rac{1 ext{ km}}{1000 m}) = 250 ext{ km}.

  • Practice Problems and Rounding:

    • Problems provided continue with unit conversions and involve rounding to correct significant figures.

2.4 The International System of Weights and Measures

  • Overview of the SI Unit System:

    • A decimal system used for measurements of mass, length, time, and other physical properties.
    • SI units often coincide with metric units but include some exceptions.
    • Comprises primary units for each measurement property with prefixes representing multiples of ten.

  • Primary Units and Common Prefixes:

    • Units used in laboratories include:
    • Mass: gram (g), milligram (mg), microgram (μg), nanogram (ng)
    • Volume: milliliter (mL), deciliter (dL), millimeter (mm)
    • Example Prefixes (shown in Table 2-1):
      | Prefix | Value | Symbol |
      |---------|---------|--------|
      | Giga | 10^9 | G |
      | Mega | 10^6 | M |
      | Kilo | 10^3 | k |
      | Hecto | 10^2 | h |
      | Deka | 10^1 | da |
      | Deci | 10^-1 | d |
      | Centi | 10^-2 | c |
      | Milli | 10^-3 | m |
      | Micro | 10^-6 | μ |
      | Nano | 10^-9 | n |
    • Units of measure conversion should only happen within the same property (e.g., volume to volume).