by Adam Feneley

Created on: May 01, 2010

The Zeroth Law of Thermodynamics

The zeroth law of thermodynamics is concerned with the idea of thermal equilibrium of two or more systems. This is commonly taken to mean equality of temperature. Strictly speaking in classical thermodynamics all systems are considered to be in equilibrium since only under these fixed conditions can one prescribe single values of volume and pressure to a system. To understand and apply the zeroth law of thermodynamics it is important to have a good understanding of what is meant by thermodynamic equilibrium. 

Essentially, for a system to be in thermodynamic equilibrium, pressure and temperature must be constant throughout the system. A simple test to find if a system is in equilibrium is to isolate it from its surroundings and check that no changes in the thermodynamic properties occur over time (heat or work transfer).  

The Zeroth law of thermodynamics states that: 

" If two systems each have the same temperature as a third system then they each have the same temperature as each other "

The zeroth law essentially states what for many seems common sense, It can be shown using a very simple example of three thermodynamic systems which we will call A, B and C. Systems A and B are placed next to each other and as such arrive at thermal equilibrium with each other (ie. They have equal temperature). Sequentially the same system A is placed next to another system C and again the two systems A and C meet equilibrium. If this is the case that A is in equilibrium with both systems B and C, it follows that systems B and C must be in thermal equilibrium with each other as well. 

An obvious practical example is the common mercury-in-glass thermometer (which we will use as system A for this example). In order to measure the temperature of something using a thermometer we assume that the mercury and glass are at thermal equilibrium with each other and the body in which they are in contact with (for a example a beaker of hot water which we will use as system B), the point when they reach equilibrium is clear since the mercury stops rising in the glass to indicate the temperature, read off the markings on the glass tube. 

If the thermometer is then withdrawn from the beaker of hot water the thermometer will cool. If we then get another beaker of hot water (this is system C) and place the thermometer inside and allow it to meet equilibrium as before we can again measure the temperature as before. If the temperature of this beaker is the same as the temperature of the first beaker then we can say that systems B and C are in thermodynamic equilibrium. 

This simple idea of comparison and equilibrium is the very statement of the zeroth law of thermodynamics. It is a handy tool when it comes to analyzing basic thermodynamic systems in a variety of science based studies from engineering and physics to chemistry and biological systems. 

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