The Zeroth Law of Thermodynamics

Introduction

** Thermodynamics is based on a few statements called laws that have broad application to physical and chemical systems.

** As simple as these laws are, it took many years of observation and experimentation before they were formulated and recognized as scientific laws.

** Three such statements that we will eventually discuss are the first, second, and third laws of thermodynamics.

** However, there is an even more fundamental idea that is usually assumed but rarely stated because it is so obvious. Occasionally this idea is referred to as the zeroth law of thermodynamics, since even the first law depends on it. It has to do with one of the variables that was introduced in the previous section, temperature.

What is temperature?

** Temperature is a measure of how much kinetic energy the particles of a system have.

** The higher the temperature, the more energy a system has, all other variables defining the state of the system (volume, pressure, and so on) being the same.

** Since thermodynamics is in part the study of energy, temperature is a particularly important variable of a system.

** We must be careful when interpreting temperature, however. Temperature is not a form of energy. Instead, it is a parameter used to compare amounts of energy of different systems.

Energy transfer between two systems

** Consider two systems, A and B, in which the temperature of A is greater than the temperature of B (Figure).

** Each is a closed system, which means that matter cannot move in or out of each system but energy can.

** The state of each system is defined by quantities like pressure, volume, and temperature.

** The two systems are brought together and physically joined but kept separate from each other, as shown. For example, two pieces of metal can be brought into contact with each other, or two containers of gas can be connected by a closed stopcock.

** Despite the connection, matter will not be exchanged between the two systems or with the surroundings.

** What about their temperatures, TA and TB ? What is always observed is that energy transfers from one system to another.

** As energy transfers between the two systems, the two temperatures change until the point where TA = TB. At that point, the two systems are said to be at thermal equilibrium.

** Energy may still transfer between the systems, but the net change in energy will be zero and the temperature will not change further.

** The establishment of thermal equilibrium is independent of the system size. It applies to large systems, small systems, and any combination of large and small systems.

** The transfer of energy from one system to another due to temperature differences is called heat.

** We say that heat has flowed from system A to system B. Further, if a third system C is in thermal equilibrium with system A, then TC = TA and system C must be in thermal equilibrium with system B also.

** This idea can be expanded to include any number of systems, but the basic idea illustrated by three systems is summed up by a statement called the zeroth law of thermodynamics:

What is the Zeroth Law of Thermodynamics?

** The zeroth law of thermodynamics states that:

"If two systems (of any size) are in thermal equilibrium with each other and a third system is in thermal equilibrium with one of them, then it is in thermal equilibrium with the other also."

** The zeroth law introduces a new idea. One of the variables that defines the state of our system (the state variables) changes its value. In this case, the temperature has changed. We are ultimately interested in how the state variables change and how these changes relate to the energy of our system.

** The final point with respect to the system and its variables is the fact that the system does not remember its previous state. The state of the system is dictated by the values of the state variables, not their previous values or how they changed.

** Consider the two systems in shown Figure:

System A: goes to a higher temperature before settling on T = 200 temperature units.

System B: goes directly from the initial conditions to the final conditions.

Therefore, the two states are the same. It does not matter that the first system was at a higher temperature; the state of the system is dictated by what the state variables are, not what they were, or how they got there.

Reference: physical Chemistry /David W. Ball / Cleveland State University /2011 .

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