Temperature and the zeroth law

Thermodynamics is now the framework that links the various functions of state. All our experimental experience can be distilled into the three laws of thermodynamics (or four, if one counts the zeroth law already mentioned in Sect. 1.1.3). Not so precisely, these three laws have been characterized as follows "In the heat-to-work conversion game the first law says you cannot win the best you can do is break even. The second law says you can break even only at absolute zero of temperature and the third law, finally, says you can never reach absolute zero." Indeed, one finds that it is difficult to win in thermodynamics. 

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. 

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. 

While sounding overly technical, we have in fact employed the zeroth law with the example of a thermometer. Let us rephrase the definition of the zeroth law and say, 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 . A medic could not easily determine the temperature of a patient without this, the zeroth law. 

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. 

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. 

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. 

The second law of thermodynamics denies the possibility of processes in which the only change is transfer of heat from a higher to a lower temperature. The zeroth law deals with thermal equilibrium and thus, by implication, the direction of heat transfer. However, the zeroth law applies only to heat transfer at a single interface, whereas the second law can deal with processes in which devices accomplish the heat transfer. These devices can have multiple interfaces with the heat reservoirs and can change during the process, as long as their change is cyclic. 

The zeroth law of thermodynamics involves some simple definition of thermodynamic equilibrium. Thermodynamic equilibrium leads to the large-scale definition of temperature, as opposed to the small-scale definition related to the kinetic energy of the molecules. The first law of thermodynamics relates the various forms of kinetic and potential energy in a system to the work which a system can perform and to the transfer of heat. This law is sometimes taken as the definition of internal energy, and introduces an additional state variable, enthalpy. 

Two systems in thermal contact eventually arrive at a state of thermal equilibrium. Temperature, as a universal function of the state and the internal energy, uniquely defines the thermal equilibrium. If system 1 is in equilibrium with system 2, and if system 2 is in equilibrium with system 3, then system 1 is in equilibrium with system 3. This is called the zeroth law of thermodynamics and implies the construction of a universal temperature scale (stated first by Joseph Black in the eighteenth century, and named much later by Guggenheim). If a system is in thermal equilibrium, it is assumed that the energy is distributed uniquely over the volume. Once the energy of the system increases, the temperature of the system also increases (dU/dT> 0). 

Like pressure and volume, temperature is a thing of everyday experience and most people think they understand it, at least to the extent of being able to say that it is a measure of how hot or cold a body is relative to our senses. Giving a precise definition is more difficult, however. Also, the scales most commonly used to measure this quantity, Celsius and (less frequently these days) Fahrenheit, are arbitrary. The thermodynamic definition, ensconced in the zeroth law, essentially states that if there is no heat flow between two bodies, they are at the same temperature. This is not very enlightening and we will have to wait until we discuss what the molecules are doing to get more insight. Nevertheless, the idea that tempera-... 

At equilibrium the two gases are at the same temperature (the zeroth law of thermodynamics), so we could, if we wanted, define the temperature to be T = (3/2). However, because the scale of temperature we use is degrees Kelvin, we need a constant of proportionality. This is k (Boltzmann s constant) when n is the number of molecules [JcT = (3 2)) and R, the gas constant, when n is the number of moles (RT - (3 2)]. If you stop and think for a moment, this result immediately gives a physical meaning to the absolute temperature as the point where molecular motion ceases. 

Tne zerutti law of thermodynamics just states tnanemperatuie exists, it s called the zeroth law because after the first, second, and third laws were already established It was realized that they depended upon a law that established the existence of temperature. 

The zeroth law of thermodynamics states "Two systems in thermal equilibrium with a third system are in thermal equilibrium with each other." The zeroth law declares that two bodies in thermal equilibrium share a thermodynamic property, and that this thermodynamic property must be a state function. The thermodynamic property described by the zeroth law is temperature. 

The thermodynamic jnstification for introducing the temperature into science is the Zeroth Law, which states that if system A is in thermal eqni-librium with system B, and system B is in thermal equilibrium with system C, then A and C wonld also be in thermal eqtiilibrium with each other, if they were pnt in contact. The third law of thermodynamics is also relevant here it states that absolnte zero (T = 0) is not attainable in a finite nnm-ber of steps, see also Chemistry and Energy Energy Heat Physical Chemistry Thermodynamics. 

From the zeroth law of thermodynamics, we know that two systems that are in thermal equilibrium with a third system are in thermal equilibrium with one another and, by definition, have the same temperature. The zeroth law is not only important in defining systems that have the same temperature, but it also provides the basic principle behind thermometry one measures temperatures of different systems by thermometers that are, in turn, compared to some standard temperature systems or standard thermometers. 

The temperature concept can be stated precisely by (1) Systems in thermal equilibrium with each other have the same temperature and (2) systems not in thermal equilibrium with each other have different temperatures. The zeroth law therefore gives us an operational definition of temperature that does not depend on the physiological sensation of hotness or coldness. This definition is in agreement with the physiological one. 

By what may seem a rather long route, the existence of a property of a system—the entropy—has been demonstrated. The existence of this property is a consequence of the second law of thermodynamics. The zeroth law defined the temperature of a system the first law, the energy and the second law, the entropy. Our interest in the second law stems from the fact that this law has something to say about the natural direction of a transformation. It denies the possibility of constructing a machine that causes heat to fiow from a cold to a hot reservoir without any other effect. In the same way, the second law can identify the natural direction of a chemical reaction. In some situations the second law declares that neither direction of the chemical reaction is natural the reaction must then be at equilibrium. The application of the second law to chemical reactions is the most fruitful approach to the subject of chemical equilibrium. Fortunately, this application is easy and is done without interminable combinations of cyclic engines. 

We state the total system is in equilibrium with respect to the energy form 1 dXi. We have omitted now the primes. If i = T and consequently Xi = S, we are talking about thermal energy. The zeroth law of thermodynamics states that in thermal equilibrium the temperatures of coupled systems are the same. As pointed out in detail, the zeroth law of thermodynamics is a special case of equilibrium, namely thermal equilibrium. 

The zeroth law of thermodynamics states that any two systems, call them A and B, that are each in thermal equilibrium with a third system, call it C, must be in thermal equilibrium with each other. Thermal equilibrium implies that the systems must have the same temperature, and therefore systems A and B must have the same temperature. This might seem totally obvious, but it is what puts our use of thermometers to compare the temperatures of different objects on a sound footing. If object C is our thermometer, we can use it to compare the temperatures of other objects. 

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. 

The most common method of temperature measurement is contact thermometry, as demonstfated in Fig. 4.1. One brings a thermometer, C, a system with a known thermal property, into intimate contact with the to be measured system, A. Next, thermal equilibration is awaited. When reached, the temperatures of A and C are equal. The use of C as a contact thermometer is based on the fact that if the two systems A and B are in thermal equilibrium with C they must also be in thermal equilibrium with each other. This statement is sometimes called the zeroth law of thermodynamics. It permits to use B with a known temperature to calibrate C, and then use C for measurement of the temperature of system A. A calibration with B can be made at a fixed temperature of a phase transition without degree of freedom, as given by the phase rule of Sect. 2.5.7. Less common are methods of temperature measurement without a separate thermometer system. They make use of the sample itself. For example, the temperature of the sample can be determined from its length, the speed of sound within the sample, or the frequency of light emitted. 

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