06.01 Temperature

Module 06 — Heat and Particles · quiz worth 15 pts

The big idea Temperature tracks average translational kinetic energy per particle. It is not the total energy in a sample, and it is not heat, which is energy transferred because of a temperature difference.

Average, total, and transfer

Three different ideas use everyday words that sound interchangeable. Separate them before doing any math.

Not sure about the basics underneath this lesson?

Reference temperatures at standard atmospheric pressure

ReferenceCelsiusFahrenheitKelvin
Absolute zero −273.15 °C −459.67 °F 0 K
Water freezes 0 °C 32 °F 273.15 K
Water boils 100 °C 212 °F 373.15 K
Before you start Review signed temperature differences, one-step algebra, and metric length units. Temperature describes an average over many particles; it is not the energy of one particle.

Temperature is an average

Temperature is proportional to the average translational kinetic energy of the particles in a substance. Two liters of boiling water and one liter of boiling water can have the same temperature because their particles have the same average kinetic energy. The larger sample has more total internal energy because it contains more particles. Heat is energy crossing a system boundary from higher temperature to lower temperature.

Temperature scales

Kelvin from Celsius
TK=TC+273.15T_K=T_C+273.15

Kelvin is the SI temperature unit. Write K, not °K.

Fahrenheit from Celsius
T_F= rac{9}{5}T_C+32

The Fahrenheit interval is 9/5 as large as the Celsius interval.

Celsius from Fahrenheit
T_C= rac{5}{9}(T_F-32)

Subtract 32 before multiplying by 5/9.

Aligned linear Celsius and Kelvin axes place boiling at 100 °C and 373 K, freezing at 0 °C and 273 K, and absolute zero at −273 °C and 0 K; the lower span is 2.73 times the upper span.
Celsius and Kelvin use equal-size intervals with different zero points. The course conversion is K = °C + 273.

Convert one scale at a time

Name the starting scale

Copy the value and unit. A bare 68 is not enough information.

Choose the equation that starts there

For 68 °F, use the Fahrenheit-to-Celsius equation before converting to kelvins.

Keep the offset separate

Temperature values need the 32 or 273.15 offset. Temperature differences do not: a change of 5 °C equals a change of 5 K.

Check the reference points

At standard atmospheric pressure, water freezes near 0 °C, 32 °F, or 273.15 K and boils near 100 °C, 212 °F, or 373.15 K.

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Linear thermal expansion

Length change
ΔL=αL0ΔT\Delta L=\alpha L_0\Delta T

ΔL and L₀ use the same length unit; α is in K⁻¹ or °C⁻¹; ΔT is in K or Celsius degrees.

Final length
Lf=L0+ΔLL_f=L_0+\Delta L

Use the sign of ΔT. Cooling normally makes ΔL negative.

Not sure about this bit?

Worked expansion example

Steel beam on a hot day

  • Original length. L0=5.0 mL_0=5.0\,\text{m}
  • Temperature change. ΔT=40.0−20.0=20.0 K\Delta T=40.0-20.0=20.0\,\text{K}
  • Steel coefficient. α=12×10−6 K−1\alpha=12\times10^{-6}\,\text{K}^{-1}

How much longer does the beam become?

  1. Use linear expansion.
    ΔL=αL0ΔT\Delta L=\alpha L_0\Delta T
  2. Substitute with compatible units.
    ΔL=(12×10−6)(5.0)(20.0) m\Delta L=(12\times10^{-6})(5.0)(20.0)\,\text{m}

ΔL = 0.0012 m = 1.2 mm.

Absolute zero

Absolute zero is 0 K, equal to −273.15 °C. It is the lower limit of thermodynamic temperature. A system at its lowest possible state has no thermal energy available to remove, but quantum systems can retain zero-point energy. The old ideal-gas extrapolation toward zero pressure or volume helped reveal this limit; real gases condense before reaching it.

Water near freezing

Liquid water reaches its greatest density near 4 °C. Cooling below that point builds a more open hydrogen-bond structure, so the volume increases. Ice is less dense than liquid water and floats, insulating the water below. Water's high specific heat also lets oceans and lakes absorb large amounts of energy with smaller temperature changes than many land materials.

Common traps

Temperature is not total kinetic energy

Temperature is an average per particle. Sample size changes total energy, not the temperature of otherwise identical samples.

Heat is not stored

A system stores internal energy. Heat names energy while it is being transferred because of a temperature difference.

Kelvin has no degree sign

Write 293 K, not 293 °K.

Use ΔT, not the final temperature

Expansion depends on Tfinal − Tinitial.

Temperature practice

Work the unit or idea before choosing. Each explanation shows the check that matters.