# Temperature measurement and Zeroth Law of Thermodynamics

Temperature measurement and Zeroth Law of Thermodynamics

Although we are familiar with temperature as a measure of "hotness" or "coldness," it is not easy to give an exact definition for it. Based on our physiological sensations, we express the level of temperature qualitatively with words like freezing cold, cold, warm, hot, and red hot. However, we cannot assign numerical values to temperatures based on our sensations alone. Furthermore, our senses may be misleading. A metal chair, for example, will feel much colder than a wooden one even when both are at the same temperature. Fortunately, several properties of materials change with temperature in a repeatable and predictable way, and this forms the basis for accurate temperature measurement. The commonly used mercury-in-glass thermometer, for example, is based on the expansion of mercury with temperature. Temperature is also measured by using several other temperature dependent properties.
It is a common experience that a cup of hot coffee left on the table eventually cools off and a cold drink eventually warms up. That is when a body is brought into contact with another body that is at a different temperature heat is transferred from the body at higher temperature to the one at lower temperature until both bodies attain the same temperature. At that point , the heat transfer stops, and the two bodies are said to have reached thermal equilibrium. The equality of temperature is the only requirement for thermal equilibrium.
The Zeroth law of thermodynamics states that
"If two bodies are in thermal equilibrium with a third body, they are also in thermal equilibrium with each other".
It may seem silly that such an obvious fact is called one of the basic laws of thermodynamics. However, it cannot be concluded from the other laws of thermodynamics, and it serves as a basis for the validity of temperature measurement. By replacing the third body with a thermometer, the Zeroth law can be restated as "Two bodies are in thermal equilibrium if both have the same temperature reading even if they are not in contact".
Thus, if we want to know if two bodies are at the same temperature, it is not necessary to bring them into contact and see whether their observable properties change with time, as described previously. It is necessary only to see if they are individually in thermal equilibrium with a third body. The third body is usually a thermometer.
The Zeroth law was first formulated and labeled by R. H. Fowler in 1931.
As the name suggests, its value as a fundamental physical principle was recognized more than half a century after the formulation of the first and the second laws of thermodynamics. It was named the Zeroth law since it should have preceded the first and the second laws of thermodynamics.
Thermometers
Any body with at least one measurable property that changes as its temperature changes can be used as a thermometer. Such a property is called a thermometric property. The particular substance that exhibits changes in the thermometric property is known as a thermometric substance.
A familiar device for temperature measurement is the liquid-in-glass thermometer, which consists of a glass capillary tube connected to a bulb filled with a liquid such as alcohol and sealed at the other end. The space
above the liquid is occupied by the vapor of the liquid or an inert gas. As temperature increases, the liquid expands in volume and rises in the capillary. The length L of the liquid in the capillary depends on the temperature. Accordingly, the liquid is the thermometric substance and L is the thermometric property.
Kelvin scale
Empirical means of measuring temperature have inherent limitations for example... the tendency of the liquid in a liquid-in-glass thermometer to freeze at low temperatures imposes a lower limit on the range of temperatures that can be measured. At high temperatures liquids vaporize, and therefore these temperatures also cannot be determined by a liquid-in-glass thermometer. Accordingly, several different thermometers might be required to cover a wide temperature interval. In view of the limitations of empirical means for measuring temperature, it is desirable to have a procedure for assigning temperature values that does not depend on the properties of any particular substance or class of substances. Such a scale is called a thermodynamic temperature scale. The Kelvin scale is an absolute thermodynamic temperature scale that provides a continuous definition of temperature, valid over all ranges of temperature. Empirical measures of temperature, with different thermometers, can be related to the Kelvin scale.
Celsius Scale
Temperature scales are defined by the numerical value assigned to a standard fixed point. By international agreement the standard fixed point is the easily reproducible triple point of water:
The state of equilibrium between steam, ice, and liquid water as a matter of convenience, the temperature at this standard fixed point is defined as 273.16 Kelvin, abbreviated as 273.16 K. This makes the temperature interval from the ice point (273.15 K) to the steam point equal to 100 K and thus in agreement over the interval with the Celsius scale discussed next, which assigns 100 Celsius degrees to it. The Kelvin is the SI base unit for temperature. The Celsius temperature scale (formerly called the centigrade scale) uses the unit degree Celsius ?C, which has the same magnitude as the Kelvin. Thus, temperature differences are identical on both scales.

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