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Zeroth Law of Thermodynamics

  • Last Updated : 05 Aug, 2021
Geek Week

One of the four laws of thermodynamics is the zeroth law of thermodynamics. The zeroth law of thermodynamics, interestingly enough, was formulated considerably later than the initial three laws. However, there was considerable debate about whether it should be referred to as the fourth law or by another name. The issue occurred because the new legislation provided a clearer definition of temperature and effectively superseded the previous three statutes. Fowler eventually came up with a name that would put an end to the argument. The concept of temperature as an indication of thermal equilibrium is framed by the Zeroth law of thermodynamics.

Zeroth Law of Thermodynamics

Consider two systems A and B, separated by a wall that does not allow any exchange of energy between them. Such a wall is known as an insulating wall or adiabatic wall. The third system C is separated from systems A and B by a conducting or diathermic wall as shown in the figure.

Zeroth Law of Thermodynamics

Since, energy can be exchanged between systems A and C, so both A and C are in thermal equilibrium. Similarly, energy can be exchanged between the systems B and C, so both B and C are also in thermal equilibrium. In other words, both systems A and B are in thermal equilibrium with the third system C separately. When the adiabatic wall between systems A and B is removed, no transfer of energy takes place between them. This shows that systems A and B are also in thermal equilibrium with each other. This observation leads to an important law known as Zeroth law of thermodynamics which is stated as follows:

Two systems A and B which are separately in thermal equilibrium with a third system C are also in thermal equilibrium with each other.

According to Zeroth law of thermodynamics, if system A is in thermal equilibrium with a system C, then



The temperature of system A = temperature of system C             …………(1)

Similarly, if system B is in thermal equilibrium with system C, then

The temperature of system B = temperature of system C             …………(2)

Now, from equations (1) and (2), we have a temperature of system A = temperature of system B. Thus, the temperature of a system or a body can be defined as follows:

The temperature of a system is a physical quantity, equality of which is the only condition for the thermal equilibrium of two systems or bodies in contact.

or

A system’s or a body’s temperature is a physical quantity that indicates whether or not the system is in thermal equilibrium with another system with which it is in touch.

Thermal Equilibrium

The zeroth law of thermodynamics recognizes that temperature is a valuable measurement since it predicts whether or not heat will flow between things. Regardless matter how the items interact, this is true. Heat can move between two things even if they are not physically interacting, as per the radiation method of heat transmission.



The zeroth law of thermodynamics says that no heat flow will occur if the systems are in thermal equilibrium.

Thermodynamics is distinguished from other studies by temperature. This trait is capable of distinguishing between hot and cold. When two or more bodies of different temperatures come into touch, they eventually reach a similar temperature and are said to be in thermal equilibrium. Even though they are in a position to transmit heat based on other considerations, systems are considered to be in thermal equilibrium if there is no heat transfer. If we store food in the refrigerator overnight, for example, the food is in thermal equilibrium with the refrigerator’s air. Thermal equilibrium occurs when heat no longer moves from the food to the air or from the air to the food.

Zeroth Law of Thermodynamics Example and Applications

The law is crucial for the mathematical formulation of thermodynamics, or, to put it another way, for expressing the mathematical definition of temperature. The most common use of this concept is to compare the temperatures of different things. If we want to accurately measure temperature, we’ll need a reference body and a characteristic of that body that changes with temperature. The change in that characteristic could be interpreted as a temperature change. The chosen feature is referred to as a thermodynamic property.

Nonetheless, Thermometers are the most prevalent application of the zeroth law of thermodynamics. Using a simple thermometer with mercury in a tube, we may witness the zeroth law in operation. Because the area of the tube remains constant as the temperature rises, the mercury expands. The height has grown as a result of this development. Now, the variation in the height of the mercury label indicates temperature changes and, in essence, aids us in measuring it.

Depending on their thermometric characteristic, several types of thermometers can be utilized. The following is a list of thermometers 

  • Constant pressure gas thermometer – Volume
  • Constant volume gas thermometer – Pressure
  • Electrical resistance thermometer – Resistance
  • Mercury-in-glass thermometer – Length
  • Thermocouple – Thermal e.m.f.

When you have two glasses of water, you have another illustration of the zeroth law of thermodynamics. One glass will be filled with hot water, while the other will be filled with cold water. If we leave them on the table for a few hours, they will achieve thermal equilibrium with the room’s temperature.

Sample Problems

Problem 1: What is the Zeroth Law of thermodynamics?

Solution:

According to the Zeroth Law of Thermodynamics, two systems that are in thermal equilibrium with a third system separately are also in thermal equilibrium with each other.

Problem 2: Body A comes into contact with body B, which then comes into contact with body C. A has a higher temperature than B, which is higher than C. According to the Zeroth Law of thermodynamics, what is the proper flow direction?



Solution:

If a body with a higher temperature comes into touch with a body with a lower temperature, the higher temperature body will transfer heat to the lower temperature body. As a result, heat will travel from point A to point B to point C, eventually reaching the same temperature.

Problem 3: Give any one application of Zeroth Law.

Solution:

Consider two different glasses of boiling water as an example. When we put a thermometer in the first cup, the water warms it up until it registers 100 degrees Celsius. We can now claim that the thermometer and the first cup of water are in thermal equilibrium. The thermometer is then placed in the second cup of boiling water, where it continues to register 100 degrees Celsius. As a result, the thermometer and the second cup of water are in thermal equilibrium. We may deduce that the two separate cups of boiling water are in thermal equilibrium with each other using the logic of the zeroth law.

Problem 4: Define temperature.

Solution:

The temperature of a system or a body is a physical quantity that determines whether the system is in thermal equilibrium with another system in its contact or not.

Problem 5: Which scale was aided by the zeroth law of thermodynamics?

Solution:

The zeroth law of thermodynamics refers to thermal equilibrium or entities that do not exchange heat. Heat flow is caused by temperature differences. As a result, this law aided in the measurement and identification of temperature as a universal attribute of matter.

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