The Zeroth Law

The zeroth law originates from the concept of thermodynamic equilibrium. A system is said to be in thermodynamic equilibrium if no spontaneous change occurs in the properties of the system such as pressure and temperature even after a small disturbance. For equilibrium, there should be no chemical reaction and no velocity gradient and the pressme and temperature should be equal at all points. Such a system is in complete balance with its surroundings. If a body at a higher temperature comes into contact with another body at a lower temperature, to attain thermodynamic equilibrium, the higher temperamre body will transfer heat to the lower temperature body until both attain and maintain the same temperature and stop further heat transfer to and from other bodies. The statement of the zeroth law is given as follows If two systems are each in thermal equilibrium with a third system, then they must be in thermal equilibrium with each other. When two bodies are in equilibrium, their temperatures will be same. 

Scottish physicist and chemist Joseph Black was the first to perceive this law. James Maxwell stated the law of equal temperatures in 1871 in the following 

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The concept of temperature derives from a fact of conmron experience, sometimes called the zeroth law of themiodynamics , namely, if tM o systems are each in thermal equilibrium with a third, they are in thermal equilibrium with each other. To clarify this point, consider the tliree systems shown schematically in figure A2.1.1, in which there are diathemiic walls between systems a and y and between systems p and y, but an adiabatic wall between systems a and p. 

Figure A2.1.1. Illustration of the zeroth law. Tluee systems with two diathemiic walls (solid) and one adiabatic wall (open).

One may note, in concluding this discussion of the second law, that in a sense the zeroth law (thennal equilibrium) presupposes the second. Were there no irreversible processes, no tendency to move toward equilibrium rather than away from it, the concepts of thennal equilibrium and of temperature would be meaningless. 

I mentioned temperature at the end of the last chapter. The concept of temperature has a great deal to do with thermodynamics, and at first sight very little to do with microscopic systems such as atoms or molecules. The Zeroth Law of Thermodynamics states that Tf system A is in thermal equilibrium with system B, and system B is in thermal equilibrium with system C, then system A is also in thermal equilibrium with system C . This statement indicates the existence of a property that is common to systems in thermal equilibrium, irrespective of their nature or composition. The property is referred to as the temperature of the system. 

The Zeroth Law of Thermodynamics An extension of the principle of thermal equilibrium is known as the zeroth law of thermodynamics, which states that two systems in thermal equilibrium with a third system are in equilibrium with each other. In other words, if 7), T2, and 77, are the temperatures of three systems, with 7j - T2 and T2 = T2, then 7j = 7Y This statement, which seems almost trivial, serves as the basis of all temperature measurement. Thermometers, which are used to measure temperature, measure their own temperature. We are justified in saying that the temperature T3 of a thermometer is the same as the temperature 7j of a system if the thermometer and system are in thermal equilibrium. 

We need to explain the bizarre name of this law, which is really an accident of history. Soon after the first law of thermodynamics was postulated in the mid nineteenth century, it was realized how the law presupposed a more elementary law, which we now call the zeroth law (see below). We call it the zeroth because zero comes before one. But scientists soon realized how even the zeroth law was too advanced, since it presupposed a yet more elementary law, which explains why the minus-oneth law had to be formulated. 

Figure 1.3 The zeroth law states, Imagine three bodies, A, B and C. If A and B are in thermal equilibrium, and B and C are in thermal equilibrium, then A and C are also in thermal equilibrium (see inset). A medic would rephrase the law, If mercury is in thermal equilibrium with the glass of a thermometer, and the glass of a thermometer is in thermal equilibrium with a patient, then the mercury and the patient are also in thermal equilibrium ...

From now on we will assume the zeroth law is obeyed each time we use the phrase thermal equilibrium . 

The zeroth law of thermodynamics says imagine three bodies, A, B and C. If A and B are in thermal equilibrium, and B and C are also in thermal equilibrium, then A and C will be in thermal equilibrium. 

The evidence for such a transfer of energy between the mouth and the ice cream is the change in temperature, itself a response to the minus-oneth law of thermodynamics (p. 7), which says heat travels from hot to cold. Furthermore, the zeroth law (p. 8) tells us energy will continue to transfer from the mouth (the hotter object) to the ice cream (the colder) until they are at the same temperature, i.e. when they are in thermal equilibrium. 

The example above illustrates how energy flows in response to the minus-oneth law of thermodynamics, to achieve thermal equilibrium. The impetus for energy flow is the equalization of temperature (via the zeroth law), so we say that the measurement is isothermal. 

In previous chapters we looked at the way heat travels from hot to cold, as described by the so called minus-oneth law of thermodynamics, and the way net movements of heat cease at thermal equilibrium (as described by the zeroth law). Although this transfer of heat energy was quantified within the context of the first law, we have not so far been able to describe why such chemical systems occur. Thermodynamic changes only ever proceed spontaneously in one direction, but not the other. Why the difference ... 

Incidentally, this argument also explains why the mouth feels cold after the ice has melted, since the energy necessary to melt the ice comes entirely from the mouth. In consequence, the mouth has less energy after the melting than before this statement is wholly in accord with the zeroth law of thermodynamics, since heat energy travels from the hot mouth to the cold ice. Furthermore, if the mouth is considered as an adiabatic chamber (see p. 89), then the only way for the energy to be found for melting is for the temperature of the mouth to fall. 

We can predict whether an ice cube will melt just by looking carefully at the phase diagram. As an example, suppose we take an ice cube from a freezer at — 5 °C and put it straightaway in our mouth at a temperature of 37 °C (see the inset to Figure 5.1). The temperature of the ice cube is initially cooler than that of the mouth. The ice cube, therefore, will warm up as a consequence of the zeroth law of thermodynamics (see p. 8) until it reaches the temperature of the mouth. Only then will it attain equilibrium. But, as the temperature of the ice cube rises, it crosses the phase boundary, as represented by the bold horizontal arrow, and undergoes a phase transition from solid to liquid. 

The zeroth law is described at http //www.sellipi.com/science/chemistry/physical/ thermodynamics/zero.html, although not in any great depth. 

Indeed, there is almost no book using the term mass spectroscopy and all scientific journals in the field bear mass spectrometry in their titles. You will find such highlighted rules, notes and definitions throughout the book. This more amusing one - we might call it the zeroth law of mass spectrometry - has been... 

Thermodynamics is a science in which the storage, transformation, and transfer of energy E and entropy S are studied. Thermodynamics is governed by four basic laws called (1) the zeroth law of thermodynamics, (2) the first law of thermodynamics, (3) the second law of thermodynamics, and (4) the third law of thermodynamics. 

The zeroth law states that if two bodies are in thermal equilibrium with a third body, they are also in thermal equilibrium with each other. 

The first step, sometimes referred to as the zeroth law of photochemistry, is the absorption of light by the carbonyl compound. There are three absorption regions in the ultraviolet for the simplest carbonyl compounds owing to the ground state to singlet n-+ a, and... 

Given this simple concept of thermal sameness or equilibrium, we can express the results of universal human observations in the following Inductive Law 3, also known as the zeroth law of thermodynamics ... 

When a hot body and a cold body are brought into physical contact, they lend to achieve the same warmth after a long lime. These two bodies are then said to be at thermal equilibrium with each other. The zeroth law of thermodynamics (R.H. Fowler) states that two bodies individually at equilibrium with a third are at equilibrium with each other. This led lo the comparison of the states of thermal equilibrium of two bodies in lei ms ol a third body called a thermometer. The temperature scale is a measure of state or thermal equilibrium, and tw-o systems at thermal equilibrium must have the same temperature. 

TEMPERATURE SCALES AND STANDARDS. That property of systems which determines whether they are in thermodynamic equilibrium. Two systems are in equilibrium when their temperatures (measured on die same temperature scale) are equal, The existence of the property defined as temperature is a consequence of the zeroth law of thermodynamics. The zerodi law of thermodynamics leads to the conclusion that in the case of all systems there exist functions of their independent properties j , such dial at equilibrium... 

The zeroth law of thermodynamics is in essence the basis of all thermometric measurements. It states that, if a body A has the same temperature as the bodies B and C, then the temperature of B and C must be the same. One way of doing this is to calibrate a given thermometer against a standard thermometer. The given thermometer may then be used to determine the temperature of some system of interest. The conclusion is made that the temperature of the system of interest is the same as that of any other system with the same reading as the standard thermometer. Since a thermometer in effect measures only its own temperature, great care must be used in assuring thermal equilibrium between the thermometer and the system to be measured. 

Heat transfer between two systems is a process that occurs at the surface of each system, and it is the propensity for this surface heat transfer that is dealt with in the zeroth law. Strictly speaking, the zeroth law only deals with the direction of heat transfer and the absence of heat transfer when the systems have finally reached thermal equilibrium with each other. During the process of heat transfer, the two systems are not at thermal equilibrium and they do not each have a unique temperature. The rate of heat transfer during the process also depends on properties of the systems, such as their thermal conductivity. 

Heat capacities can be defined for processes that occur under conditions other than constant volume or constant temperature. For example, we could define a heat capacity at constant length of a sample. However, regardless of the nature of the process, the heat capacity will always be positive. This is ensured by the zeroth law of thermodynamics, which requires that as positive heat is transferred from a heat reservoir to a colder body, the temperature of the body will rise toward that of the reservoir in approaching the state of thermal equilibrium, regardless of the constraints of the heat-transfer process. 

The thermal energy of a high-temperature object can be transferred to a lower-temperature object by a flow of heat. Heat will not, however, spontaneously flow from a lower to a higher temperature. Of course, because we used the direction of heat flow to define temperature, this is just a reiteration of the zeroth law. 

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