4.1 - Thermal Equilibrium

Thermal Contact and Thermal Equilibrium

Two bodies are in thermal contact when heat energy can pass between them, such as a cold metal spoon placed in hot coffee.
Initially, the hotter body transfers heat to the colder body at a higher rate than heat flows in the opposite direction. The net heat transfer is from hot to cold.
The hotter body cools while the colder body warms until both have the same temperature.
At thermal equilibrium, heat transfer rates in both directions are equal, so net heat transfer is zero.

Situation	Heat transfer
Baking a cake	Hot oven air transfers heat to the cake batter, heating it until baked.
Clinical thermometer	Heat flows from the patient’s body to the thermometer until their temperatures match; the reading then gives body temperature.
Refrigerating food	Food releases heat to the colder refrigerator air until thermal equilibrium is reached.
Cooling a drink with ice	Ice absorbs heat and melts; the melted ice continues absorbing heat until thermal equilibrium is reached.

A thermometric property is a measurable physical property that changes with temperature, such as the length of a liquid column.
Calibration establishes a thermometer’s scale using two fixed temperature points:
- Lower fixed point: melting ice, $0^{\circ} C$ .
- Upper fixed point: boiling distilled water, $100^{\circ} C$ .
Mark each liquid level only when it stops changing. Divide the distance between the two marks into 100 equal divisions to measure temperatures between $0^{\circ} C$ and $100^{\circ} C$ .
Let $L_{100}$ be the column length measured from the $0^{\circ} C$ mark to the $100^{\circ} C$ mark, and $L_{θ}$ the length from the same zero mark to the unknown-temperature level:

θ = \frac{L _{θ}}{L _{100}} \times 100^{\circ} C

The thermometer bulb must not touch the base or side wall of the beaker during measurement.
Periodic calibration matters for cooking thermometers because food preparation depends on control of temperature and time.