Zeroth Law of Thermodynamics & Absolute Temperature - Thermodynamics - Mechanical

Zeroth Law of Thermodynamics and Absolute Temperature

Thermometers with liquid working fluids are commonly used for measurement of temperature. When such a device is brought into contact with a body whose temperature is to be measured, the liquid column inside the thermometer expands due to heat conducted from the body. The expanded length of the liquid column provides a quantitative indication of the degree of hotness. Different thermometric substances expand differently under the same temperature change; this is why the choice of thermometric property matters for defining a reliable temperature scale.

Zeroth Law of Thermodynamics

Statement

Zeroth Law of Thermodynamics: If two bodies are in thermal equilibrium with a third body, then the two given bodies will be in thermal equilibrium with each other.

Explanation and significance

Thermal equilibrium means there is no net heat flow between bodies when they are placed in thermal contact. The zeroth law asserts a transitive relation of thermal equilibrium. Its practical significance is that it allows the use of a thermometer (the third body) to compare temperatures of other bodies. If body A and a thermometer T are in equilibrium, and body B and thermometer T are in equilibrium, then A and B are at the same temperature even if A and B have not been brought into direct contact.

Thermometers and thermometric properties

• Thermometric property is any physical property that changes with temperature (for example, length of a liquid column, electrical resistance, volume or pressure of a gas, thermoelectric voltage).
• For a thermometric property to form the basis of a temperature scale it should vary monotonically with temperature and be reproducible.
• Different thermometric substances give different numerical readings for the same physical temperature unless the thermometric property is related to a universal standard. That is why a standard or ideal thermometer is needed to establish an absolute scale.

Temperature Scales and Fixed Points

Celsius scale (empirical scale)

The Celsius scale uses two convenient fixed points of water at standard atmospheric pressure:

• Ice point (freezing point) - freezing point of water is assigned the value 0 °C.
• Steam point (boiling point) - boiling point of pure water is assigned the value 100 °C.
• The distance between these two fixed points on the thermometric device is arbitrarily divided into 100 equal parts called degrees. The scale can be extended below 0 °C and above 100 °C as required.

Limitations of empirical scales

• Readings depend on the thermometric substance; different substances give different numerical values for the same physical temperature unless appropriately standardised.
• Standard atmospheric pressure must be specified for the steam point to be reproducible.

Absolute (Thermodynamic) Temperature and the Gas Thermometer

Choice of an ideal thermometric substance

To obtain a temperature scale independent of the particular substance used, an ideal gas has been chosen as a reference thermometric substance. An ideal-gas thermometer uses a gas whose pressure or volume at fixed geometry varies in a simple, nearly linear way with temperature. By extrapolating gas behaviour to appropriate limits, one can define a scale that is independent of the working substance.

Kelvin scale and relation to Celsius

The SI thermodynamic (absolute) temperature scale uses the unit kelvin (K). The relation between temperature on the Kelvin scale and the Celsius scale is

T (K) = 273.15 + t (°C)

Thus 0 K corresponds to -273.15 °C, which is called absolute zero - the theoretical lower limit of the thermodynamic temperature scale.

Triple point of water (practical fixed point)

For accurate calibration of thermometers, the triple point of water (the unique condition where ice, liquid water and vapour coexist in equilibrium) is used as a precise fixed point. The triple point has been assigned a value in the Kelvin scale used for practical calibrations. In precise metrology the triple point is often used instead of the boiling point because it is less sensitive to pressure variations.

Derivation idea using ideal gas (conceptual)

Using the ideal gas law at fixed volume or fixed pressure, the thermodynamic temperature can be related to measurable quantities such as pressure or volume. Conceptually, by extrapolating the linear relation between pressure (at constant volume) and temperature to the pressure value that would correspond to zero pressure, one obtains the intercept corresponding to absolute zero. This provides the conceptual basis for defining the zero of the Kelvin scale.

Worked examples

Example 1 - Convert 25 °C to kelvin

Sol.

T (K) = 273.15 + t (°C)

T (K) = 273.15 + 25

T (K) = 298.15 K

Example 2 - Convert -40 °C to kelvin

Sol.

T (K) = 273.15 + t (°C)

T (K) = 273.15 + (-40)

T (K) = 233.15 K

Practical applications and engineering relevance

• Temperature measurement and instrumentation: The zeroth law underpins the operation of all practical thermometers and temperature sensors (liquid-in-glass thermometers, resistance thermometers, thermocouples, gas thermometers, thermistors).
• Calibration and standards: Fixed points (ice point, triple point, steam point) provide references for calibration of instruments used in civil and mechanical engineering practice.
• Heat flow and thermal analysis: Knowing absolute temperature is essential for thermodynamic calculations, heat-transfer analysis, and material property evaluations.
• Design of thermal systems: Accurate temperature measurement and consistent scales are essential in the design and testing of HVAC, power plants, refrigeration systems, engines and structural materials exposed to temperature gradients.

Summary

The zeroth law of thermodynamics establishes that thermal equilibrium is a transitive relation and provides the basis for using a thermometer as a common reference. Empirical scales such as the Celsius scale use convenient fixed points of water, while the Kelvin scale gives an absolute temperature measure independent of the thermometric substance. The relation T (K) = 273.15 + t (°C) connects the two scales, and absolute zero (0 K = -273.15 °C) is the lower limit of temperature on the thermodynamic scale.