11. Temperature (A-level) Notes (Thermal Equilibrium, Scales, and Thermometers)

Thermal energy flows from an area of higher temperature to an area of lower temperature when objects are in thermal contact.
Energy transfer continues until the objects reach the same temperature, i.e., thermal equilibrium.
Zeroth law of thermodynamics: if object A is in thermal equilibrium with object B, and object B is in thermal equilibrium with object C, then A is in thermal equilibrium with C.
Practical implication: thermal equilibrium defines a common temperature reference for connected bodies; energy exchange ceases when equilibrium is reached.

Many physical properties vary with temperature and can be used to measure temperature, such as:
- Change in resistance of a metallic conductor or semiconductor (e.g., thermistor).
- Voltage produced across a thermocouple.
- Change in volume of a liquid.
- Change in volume of a gas at constant pressure.
- Change in pressure of a gas at constant volume.
Kelvin scale (thermodynamic temperature scale): the Kelvin scale is an absolute scale that does not depend on the property of any substance.
Celsius scale: depends on the melting point (0° C) and boiling point (100° C) of pure water at atmospheric pressure.
Absolute zero: 0 K on the Kelvin scale; the temperature at which particles have no kinetic energy and the volume and pressure of a gas would be zero.
All equations in thermal physics use temperature measured in kelvin (K).
A change of 1 K is equal to a change of 1 °C, i.e., temperature differences are the same in both scales.
Conversion between scales:
- $K = C + 273.15$
- Where K is temperature in kelvin and C is temperature in Celsius.
Useful equivalent: 0 °C = 273.15 K; -273.15 °C corresponds to 0 K (absolute zero).

Many physical properties vary with temperature, leading to different thermometer types that rely on different properties.
A thermocouple is a type of thermometer with a specific structure:
- The reference junction is kept at a constant temperature, while the measurement junction is used to measure an unknown temperature.
- If there is a temperature difference between the junctions, an emf is formed, which is measured by the voltmeter.
- The temperature is calculated from the recorded emf using a calibration curve.
A thermistor is a semiconductor thermometer:
- Its temperature decreases as its resistance increases (negative temperature coefficient).
- The resistance can be measured and then converted to temperature using a calibration curve.
Both have advantages and disadvantages, summarized in the comparison below.

Feature: Sensitivity
- Thermocouple: Sensitivity depends on the choice of metals in the two wires; can be made very sensitive.
- Thermistor: Very sensitive but over a narrow temperature range.
Feature: Range
- Thermocouple: Large temperature range.
- Thermistor: Narrow temperature range.
Feature: Response time
- Thermocouple: Junctions have small thermal capacity, so response time is short.
- Thermistor: Larger thermal capacity, so response time is longer.
Feature: Stability
- Thermocouple: Wires forming the junctions are subject to corrosion and aging effects may occur.
- Thermistor: Very stable and mostly unaffected by aging.
Feature: Ease of use
- Thermocouple: The reference junction must be kept at a constant temperature (often with ice water), which can be awkward; modern thermocouples have improved temperature compensation, making them easier to use.
- Thermistor: Generally easier to use.
Note: An image in the original material shows the thermocouple structure with a reference junction and a measurement junction, and how emf arises from the temperature difference.