Notes on Temperature Scales, Density, Volume, and Related Calculations

The Kelvin: A Measure of Temperature

  • Kelvin (K) is the SI unit of temperature.

  • Temperature is a measure of the average kinetic energy of the atoms or molecules that compose a sample of matter.

  • Temperature also determines the direction of thermal energy transfer; heat transfers from hot objects to cold ones.

  • Three common temperature scales:

    • Fahrenheit (∘F^{\circ}F)

    • Celsius (∘C^{\circ}C)

    • Kelvin (K)

Converting between Temperature Scales

  • Converting between Celsius and Fahrenheit:

    • ∘C=∘F−321.8^{\circ}C = \dfrac{^{\circ}F - 32}{1.8}

  • Converting Celsius to Kelvin:

    • K=∘C+273K = ^{\circ}C + 273

Example: Converting a fever from Fahrenheit to Celsius and Kelvin

  • A sick child has a temperature of 104.0°F. What is the temperature in:

    • (a) °C

    • (b) K

  • (a) Convert to °C:

    • ∘C=104.0−321.8=40^{\circ}C = \dfrac{104.0 - 32}{1.8} = 40

  • (b) Convert to K:

    • First, use °C value: K=∘C+273=40+273=313 KK = ^{\circ}C + 273 = 40 + 273 = 313\,K

Prefix Multipliers

  • The International System of Units uses prefix multipliers with the standard unit.

  • These multipliers change the value of the unit by powers of 10.

  • Base unit refers to the base unit without prefixes (e.g., meter, second, gram).

  • Common prefixes include kilo- (10310^3), milli- (10−310^{-3}), micro- (10−610^{-6}), nano- (10−910^{-9}), etc.

Derived Units: Volume and Density

  • A derived unit is a unit that is a combination of other base units.

  • Example: the SI unit for speed is meters per second, m s−1\mathrm{m\,s^{-1}}, formed from meters and seconds.

  • Two common derived units in chemistry:

    • Volume: base unit is m3\mathrm{m^{3}}

    • Density: base unit is kg m−3\mathrm{kg\,m^{-3}}

  • Commonly used volume units include cubic meters, cubic centimeters, and liters:

    • m3, cm3, mm3\mathrm{m^{3}},\ \mathrm{cm^{3}},\ \mathrm{mm^{3}}

    • Also, liter and milliliter: L, mL\mathrm{L},\ \mathrm{mL}

Volume

  • Volume is a measure of space.

  • Any unit of length cubed yields a volume unit:

    • m3\mathrm{m^{3}}

    • cm3\mathrm{cm^{3}}

    • mm3\mathrm{mm^{3}}

  • In chemistry, common volume measurements include liters (L) and milliliters (mL).

Density

  • Density (d) is the ratio of mass (m) to volume (V):

    • d=mVd = \dfrac{m}{V}

  • Related forms:

    • Mass in terms of density and volume: m=d⋅Vm = d\cdot V

Density: Properties and Implications

  • Density is a characteristic physical property that depends on temperature.

  • Density is an example of an intensive property (independent of the amount of the substance).

  • In contrast, mass is an extensive property (depends on the amount of the substance).

Calculating Density

  • Practical example: determining whether a ring is platinum by density.

  • Given:

    • Mass, m=3.15 gm = 3.15\,\text{g}

    • Volume displaced by water, V = 0.233\,\text{cm^{3}}

  • Calculation:

    • d = \dfrac{m}{V} = \dfrac{3.15\,\text{g}}{0.233\,\text{cm^{3}}} \approx 13.5\,\text{g cm^{-3}}

  • Interpretation:

    • The calculated density is approximately 13.5\,\text{g cm^{-3}}.

    • Typical platinum density is around \approx 21.5\,\text{g cm^{-3}} (at room temperature).

    • Therefore, based on this measurement, the ring is unlikely to be made of platinum.