Temperature and Heat

Temperature as State

absolute kelvin readings

Temperature is a state variable: it fixes the thermal condition of a body independently of how that condition was reached. The kelvin scale is anchored at absolute zero and made reproducible through fixed points such as the triple point of water. A thermometer reading is a model-mediated inference from a measurable response (volume, resistance, emitted radiation), not the microscopic motion itself.

Temperature is a state variable. Differences in kelvin measure how far apart two thermal states are. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Read absolute temperatures

Temperature is a state reading. These thermometers read 300 kelvin and 330 kelvin.

Tcool=300 KTwarm=330 KT_{\text{cool}} = 300\ \text{K}\qquad T_{\text{warm}} = 330\ \text{K}
Kelvin thermometersTwo thermometer states are shown on one absolute scale.300 Kcool330 Kwarm

Compare the state readings

The warmer state is higher by 30 kelvin. The difference is a temperature interval.

ΔT=330 K−300 K=30 K\Delta T = 330\ \text{K} - 300\ \text{K} = 30\ \text{K}
Kelvin thermometersTwo thermometer states are shown on one absolute scale.300 Kcool330 Kwarm

Differences come from pairs of states

The diagram shows the first row. A temperature interval is always a subtraction between two absolute kelvin readings, not a third thermometer substance.

TcoolTwarmΔT300 K330 K30 K305 K330 K25 K300 K360 K60 K\begin{array}{c|c|c}T_{\text{cool}}&T_{\text{warm}}&\Delta T\\300\ \text{K}&330\ \text{K}&30\ \text{K}\\305\ \text{K}&330\ \text{K}&25\ \text{K}\\300\ \text{K}&360\ \text{K}&60\ \text{K}\\\end{array}
Kelvin thermometersThe first table row is the checked diagram.300 Kcool330 Kwarm