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Temperature is one of the most important concepts in science. When describing characteristics of any system including the body of a living organism, mechanical system, chemical system, any substance, or planetary system, properties of that system are used. Among those properties, temperature plays an important role. The zeroth law of thermodynamics is responsible for the introduction of this important thermodynamic property, temperature.

But before the introduction of the zeroth law, people are familiar with the concept of temperature. Even thermometers were invented before the introduction of this law. That is why the zeroth law is known as the commonsense law. Even though people were familiar with this concept, scientists decided to introduce the concept as a law. When that happened, the first and second laws of thermodynamics were well established. But because the zeroth law is more fundamental than the other two, they assign it as the zeroth law.

The zeroth law of thermodynamics

If system A is in thermal equilibrium with system B and also system A is in thermal equilibrium with system C, then system B and C are in thermal equilibrium with each other.

The Zeroth Law of Thermodynamics
Figure 01: The Zeroth Law of Thermodynamics

The above concept is known as the zeroth law of thermodynamics.

Thermodynamic equilibrium

Simply equilibrium means, the state of balance between two or more systems. That means those systems will be in a stable and balanced state.

If no change in any macroscopic properties is observed in a system that is isolated from its surrounding, that system is in a state of thermodynamic equilibrium. An isolated system always reaches the state of thermodynamic equilibrium over time and that system never leaves that state of thermodynamic equilibrium spontaneously.

For a system to be in the state of thermodynamic equilibrium, the following conditions should be satisfied.

a. Mechanical equilibrium

For a system to be in mechanical equilibrium, all the forces within the system and between the system and its surrounding are balanced. If there are any unbalanced forces present, either the system alone or both the system and its surrounding undergo change until the system reaches the mechanical equilibrium.

b. Chemical equilibrium

For a system to be in chemical equilibrium, there shouldn’t be any chemical reaction (the net amount of reactants and products should be constant) or shouldn’t be any matter transfer (ex: diffusion) within part of the system.

c. Thermal equilibrium

A system that is surrounded by a diathermic wall, exists in states of both mechanical and chemical equilibriums and if that system shows no spontaneous change in any property of the system, that system has attained the state of thermal equilibrium.

Any system that failed to satisfy any of the above three conditions, that system is in a non-equilibrium state.

Measurement of temperature

The zeroth law is the basic concept behind the measurement of temperature. Temperature is the thermodynamic property of a system that helps to determine that system is in thermal equilibrium with other systems. A reference body is used to get a quantitative measurement of temperature. This reference body should have distinguishable physical characteristics/properties that change with the temperature.

This reference body used to measure temperature quantitatively is called a ‘thermometer’. The property that a thermometer has those changes with temperature is known as the ‘thermometric property.’

The thermometer is important to measure the temperature of a system. When a thermometer is placed contacting a system that is needed to measure temperature, the thermometer, and the system will be reached thermal equilibrium. So, the temperatures of both systems will be equal. Using the temperature scale in the thermometer, temperature readings can be observed.

Thermometric properties

So, by observing the change of this thermometric property to changing temperature, the temperature can be measured quantitatively. When selecting a good thermometric property for observing temperature reading accurately, it should have some important qualities.

  • The property should vary continuously with the temperature in the range of operating
  • The variation of the property should show a linear relationship with the temperature in the range of operation (variation should be uniform)
  • The variation of the property should be measurable, and it should have high sensitivity
  • The effect on the system that needs to measure temperature should be negligible (for example thermometric liquids that use in thermometers should have a very low heat capacity)

Using this concept, there are many types of thermometers are available.

ThermometerThermometric property
ThermocoupleElectromotive force
Electrical resistance thermometerResistance
liquid-in-glass thermometerExpansion of liquid (change in length)
Constant pressure gas thermometerVolume
Constant volume gas thermometerPressure
Table 01: Thermometric properties used in thermometers

Temperature scales

To assign a temperature value for a body/ system, a scale for the temperature is required. 

Let’s find out how to measure temperature using changes in thermometric properties in thermometers. 

  • X – the value of the thermometric property
  • θ – temperature of the system that surrounds the thermometer
  • a - arbitrary constant

The temperature of the system, θ is a function of thermometric property, X. So, let’s indicate this function as θ(X), and also let’s assume that the function is linear.

The Zeroth Law of Thermodynamics eq 01

Before 1954, two fixed points were used to calibrate a thermometer. Those points were the ice point of water and the steam point of water.

  • Ice point (i) – the temperature of pure ice that coexists in equilibrium with air-saturated water at standard atmospheric pressure
  • Steam point (s) – the temperature of pure steam in equilibrium with pure water at standard atmospheric pressure

A fixed point in a temperature scale means, ‘the value of temperature that is assigned to an easily reproducible state of a system’.

The Zeroth Law of Thermodynamics eq 02

But after 1954, only one fixed point is used because the two fixed points that were used before are not reliable.

  • At ice points, it is difficult to maintain equilibrium between pure ice and air-saturated water because when the ice melts, ice will be surrounded by pure water. So, it prevents ice from contacting air-saturated water.
  • At the steam point, pressure will be changed because of the release of water vapor.

As a solution for this, the triple point of water has been introduced as a fixed point. The triple point of water is the state where ice, liquid water, and water vapor coexist in equilibrium. So, since 1954, only one fixed point is used to calibrate thermometers. The value of this point is assigned as 273.16 Kelvin (273.16K) (relative to the absolute zero – 0K). Because this fixed point is easily reproducible, the triple point (tp) of water is the standard fixed point of thermometry.

The Zeroth Law of Thermodynamics eq 03

The above principle can be applied to measure temperatures using different thermometers. (Table 02)

Celsius scale of temperature (0C)

  • The name of this scale is given as Celsius in 1948 to honor Swedish astronomer Anders Celsius. (He developed a similar temperature scale in 1742.) Before that this scale was known as the centigrade scale.
  • Since 1743 this scale is based on the freezing point (00C) and boiling point (1000C) of water at 1atm pressure. Before that boiling point was considered 00C and the freezing point was considered 1000C. In 1743 that was reversed.
  • Recently based on an international agreement this scale was redefined using absolute zero (-273.150C) and the triple point of water (0.010C).

Fahrenheit scale of temperature (0F)

  • This scale was based on a proposal by physicist Daniel Gabriel Fahrenheit in 1724.
  • Later, 2 fixed points were used in this scale; 320F – the freezing point of pure water at sea level and standard atmospheric pressure, 2120F – the boiling point of water at sea level and standard atmospheric pressure

Kelvin scale of temperature (K)

  • This is the SI base unit for temperature. This temperature is an absolute thermodynamic temperature scale. So, the Kelvin scale uses absolute zero as its null point. (0K)
  • This scale was defined using the Boltzmann constant.
  • The Kelvin scale was named after engineer and physicist William Thomson, 1st Baron Kelvin.

Relationship between the Celsius scale and Fahrenheit scale

Using the below equation temperatures can be converted between these two scales.

  • C – Celsius scale temperature
  • F- Fahrenheit scale temperature
The Zeroth Law of Thermodynamics eq 04

Relationship between the Celsius scale and Kelvin scale

  • T – Temperature on the Kelvin scale
  • t – Temperature on the Celsius scale
The Zeroth Law of Thermodynamics eq 05


If a temperature of a given system was measured by using a few different types of thermometers at the same time, readings obtained from them will be different by a considerable amount. The smallest variation between readings will be observed from gas thermometers. So that is the reason behind choosing gas as the standard thermometric substance. So, because of its highly accurate measurements, the Constant Pressure Gas Thermometer is used to calibrate other thermometers.

ThermometerSymbol of the Thermometric property usedTemperature measurement (θ) according to equation 7
θ =
Thermocoupleε (Electromotive force)273.16(ε/ εtp)
Electrical resistance thermometerR (Resistance)273.16(R/ Rtp)
liquid-in-glass thermometerL (change in length)273.16(L/ Ltp)
Constant pressure gas thermometerV (Volume)273.16(V/ Vtp)
Constant volume gas thermometerP (Pressure)273.16(P/ Ptp)
Table 02: types of thermometers

When making a good thermometer there are many important concepts involved such as the thermal expansion of solids, liquids, and gases, the concept of ideal gases, the effect of the temperature on resistance, and electromotive force. They will be discussed in different articles. Also, the concepts behind different thermometers will be discussed differently.

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References and Attributes

Atkins, P. Four laws that drive the universe; Oxford University Press: Oxford, 2007.

Nag, P. Basic and applied thermodynamics; Tata McGraw-Hill: New Delhi, 2010.


The cover image was created using an image by Mudassar Iqbal from Pixabay

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