Talk:Scale of temperature/Archive 1

Article is duplicate of existing material
This article should be considered for deletion because it is essentially a copy of the articles on temperature without any new information. Whatever little appears new is unreferenced and appears as original research and provides no context or basis to the rest of the articles which are presumably taken as examples of scales. There is no justification given why this article on temperature scales is somehow different that the article on temperature. Kbrose (talk) 04:15, 26 October 2010 (UTC)


 * If it is on 'temperature scales', then there are several meanings that are independent of 'temperature'. The first is that the various fixed temperatures have changed over time, both in nature and value.  These points create some sort of linear scale, whereapon one can simply substitute something like "°C = 100 - °De/1.5" has a purely numeric relation.


 * There is little point in delving into what temperature might mean, like there would be no great need to delve into the meanings of length when discussing a measurement system. There ought be a page for 'length (measure)', different to BI length units.  Wendy.krieger (talk) 09:19, 3 August 2012 (UTC)

Ideal gas problem
You write here "When pressure approaches zero, all real gas will behave like ideal gas". Why do you say this? Diatomic and monatomic gases behave differently in these conditions because they have different numbers of degrees of freedom. --Damorbel (talk) 08:08, 19 October 2010 (UTC)


 * They have different degrees of freedom but they both behave like ideal gas. Is that a contradiction?--Netheril96 (talk) 08:52, 19 October 2010 (UTC)


 * It is a contradiction. Ideal gases comprise particles that only interact by elastic collision, the only energy possessed by the particles of an ideal gas are the translational motions of the particles. In contrast non ideal gases, such as those with diatomic molecules like N2, have vibrational energy stored in the (elastic) force binding the two (or more) (massive) atoms making up the molecule. This mass and elastic force make up a resonant energy storage unit which, like the translational momentum, stores additional energy proportional to temperature, thus the particles of non ideal gases store more thermal energy than monatomic gases. 'Real gases' made up of monatomic atoms are much closer to 'ideal' gases than others because 'Real' monatomic gases have interatomic forces that cause their behaviour to deviate from the model behaviour e.g. an ideal gas has nothing to make it liquify or freeze; even Helium will liquify and, given enough pressure, solidify. --Damorbel (talk) 12:00, 20 October 2010 (UTC)


 * The particles ideal gas comprises are molecules, not atoms. Monatomic and diatomic gases have different molar heat capacity, but they both observe ideal gas law when they are thin enough for interactions between molecules to be negligible.--Netheril96 (talk) 01:48, 21 October 2010 (UTC)


 * Netheril96 is right. If a fixed amount of gas has PV proportional to T, then it is an ideal gas. As you lower the density, the intermolecular forces become less and less important. The lower the density, the more the gas behaves like an ideal gas. The present ideal gas article is incorrect when it says that the specific heat of an ideal gas is constant. The specific heat, which is a measure of the total energy stored in a molecule, may be any number, and may vary with temperature. PAR (talk) 16:39, 21 October 2010 (UTC)

Zeroth law problem
The zeroth law only applies to three systems thermally connected in a "chain" A-B-C. If A~B and B~C then A~C. If you have 3 bodies which are not thermally connected, and then you connect A and B and allow equilibrium to occur, then A~B. If you disconnect A and B, and then bring B and C into equilibrium, then B~C. This does NOT mean that now A~C. Suppose you have three bodies A,B,C with the same "thermal mass", with temperatures of 10, 20, and 30 degrees C respectively. Bring A and B to equilibrium, their temperature will be (10+20)/2=15 degrees. Now bring A and C into equilibrium, their temperature will be (15+30)/2=22.5 degrees. B and C now have temperatures of 15 and 22.5 degrees - they are not in thermal equilibrium. The zeroth law only applies to 3 bodies thermally connected as A-B-C. PAR (talk) 16:39, 21 October 2010 (UTC)


 * The equivalence relation here is to be in thermal equilibrium the instant they contact. If they need time to achieve thermal equilibrium, they are not equivalent.--Netheril96 (talk) 08:33, 22 October 2010 (UTC)


 * Ok, good. But this really brings out the problem of how do you know when thermal equilibrium exists when you do not have a thermometer? The zeroth law is of no help on this. This is where the second law is needed in order to detect when two systems are in thermal equilibrium, and is vital to the definition of temperature. PAR (talk) 13:36, 22 October 2010 (UTC)


 * This is the first time I have heard of the indispensable role of second law in defining temperature. Is this just your thought or what your textbooks say? And how does second law tell you whether or not two system are in thermal equilibrium?--Netheril96 (talk) 17:04, 22 October 2010 (UTC)


 * The book "Thermodynamics" by Enrico Fermi is excellent, and it is outlined in this book. (Small book 3/8" thick). The procedure is also outlined in the Thermodynamic temperature article. But don't take my word, or the word of the textbooks. The question that must be answered is - how do we define temperature? That is the same as "how do we build a thermometer?". If all you know is the zeroth law, you cannot build a thermometer, because you cannot determine when two systems are in thermal equilibrium. The second law provides the concept of the reversible heat engine. This is a powerful thing. It connects many mental ideas to actual measureable quantities. A reversible engine operates between two different "reservoirs" and delivers measurable work. If the reservoirs are in thermal equilibrium, it delivers zero work. If they are not, then it will deliver positive or negative work. Measuring the work delivered in the cycles of the engine allows you to specify a temperature for each reservoir. It provides an "order relationship" for temperature, to speak mathematically. It can also be shown that the ratio of the work into the engine to the work out (both measureable) is equal to the ratio of the temperatures. NOW we have a practical, measurable definition of absolute temperature, to within a multiplicative constant. The reversible engine is the thermometer we have been looking for. PAR (talk) 20:07, 22 October 2010 (UTC)


 * I have stated in the article clearly that your definition is thermodynamic temperature. So basically you still don't understand the difference between thermodynamic and just temperature. Thermal equilibrium happens whenever macroscopic variables cease to change. Constructing a thermometer is easy&mdash;for example, just as I say in the article, a tube with mercury. If mercury ceases to expand or constrict, it is in thermal equilibrium with the measurand and its volume can be taken to reflect temperature. Maybe you should read ITS-90 again because that is obviously not defined with reversible engines.--Netheril96 (talk) 00:07, 23 October 2010 (UTC)


 * Thermodynamic temperature is the only true absolute temperature. Every other temperature scale is an attempt to match thermodynamic temperature. If these other temperature measuring methods do not agree with thermodynamic temperature, then they are "wrong" to that extent. If you make a thermometer out of mercury and mark off 100 equally spaced points between the boiling point and the freezing point of water, it will be wrong, because mercury does not expand exactly linearly with thermodynamic temperature. But this "linear mercury thermometer" is very close. One of the reasons they changed the Celsius scale to be 0.01 at the triple point of water instead of 0.00 at the freezing point is because the triple point of water is a lot more stable and reproducible than the freezing point. Stable with respect to what? With respect to the thermodynamic temperature. The ITS-90 is an attempt to match thermodynamic temperature over a wide range of temperatures. As soon as sombody can come up with a closer match to thermodynamic temperature, the ITS-90 will become obsolete, or will be modified, just like the Celsius scale was. Thermodynamic temperature will never be modified or become obsolete. The first sentence in the "Details" section of ITS-90 says "ITS-90 is designed to represent the thermodynamic (absolute) temperature scale (referencing absolute zero) as closely as possible throughout its range." There is no such thing as "just temperature", any more than there is a difference between a true straight line and "just a straight line". A ruler does not define a straight line, a straight line is something a ruler tries to reproduce. Every temperature scale other than the thermodynamic scale does not define a temperature, they are attempts to reproduce the thermodynamic temperature.


 * I agree, if you take a linear (i.e. slightly inaccurate) mercury thermometer, and it ceases to change, then it is in thermal equilibrium with the contacted body. I also agree that if I measure the temperature of two separate bodies with the same linear mercury thermometer, and the readings match, then they are in thermal equilibrium, by the zeroth law. You are right about that. But this is only because it has been shown that mercury could be used as the working body in a reversible engine. And if we did use it, and calculated the temperature from that reversible engine, it would not agree exactly with the linear mercury thermometer. The answer would not be to define temperature by the linear mercury thermometer, but rather to move the marks on the thermometer until they matched the results of the reversible engine. Then you would have a very accurate, but not linear, mercury thermometer. PAR (talk) 01:49, 23 October 2010 (UTC)

So in your dictionary, temperature is the synonym for thermodynamic temperature; any other scales are "fake" or "approximate" scales. So the International Temperature Scale of 1990 is not a temperature scale but just an approximation method for thermodynamic temperature? Then that is just a problem of definition or convention.--Netheril96 (talk) 04:58, 23 October 2010 (UTC)


 * Yes, temperature is a synonym for thermodynamic temperature. Thermodynamic temperature is like a straight line. You want to keep clear the difference between a straight line and a ruler. A physical ruler does not define a straight line. Geometry tells you that if you build a number of perfect rulers and bring them together they will all touch each other everywhere along their length. That means they are straight. Geometry does not tell you what the unit of distance is, you pick that yourself - a meter, a foot, whatever. If you mark off a distance on a ruler, then you have a distance scale. But there is no such thing as a perfect ruler. You build a ruler, mark off a distance, and then you build other rulers that seem to be straight, and the marks seem to match, and you say you have a good ruler. But then you develop new technology, a better microscope that shows that the rulers do not touch everywhere, and the marks do not match up. Now you have to develop a new ruler, a new distance scale, so that the rulers look straight again, and the marks match up. Now you have a good ruler again. But tomorrow, maybe not.


 * Thermodynamic temperature is like the straight line, a thermometer is like a ruler. The second law tells you that if you build a perfectly reversible heat engine, the ratio of the work done on the two power cycles will equal the ratio of the thermodynamic temperatures of the two reservoirs driving the engine. The second law does not tell you what the unit of temperature is, you pick that yourself, and then you have a temperature scale. But there is no such thing as a perfectly reversible heat engine. You build a thermometer, mark off your step size by picking two points like the freezing and boiling point of water. If different people build the same thermometer and the readings match and the temperature differences match, then you say you have a good thermometer. But then new technology comes along which shows that the temperatures don't match, and now you have to build a better thermometer. Thats what happened with the old Celsius scale. First they define 100 degrees as the temperature difference between freezing and boiling water. But then they notice that the freezing point seems to jump around, the measurements don't match. So they make a new scale with the lower end being defined as 0.01 at the triple point of water, which does not seem to jump around. Its a new scale, just as good as the old scale, but better defined experimentally. The better and better your thermometer becomes, the more accurately it measures the thermodynamic temperature in whatever scale you have chosen.


 * The ITS-90 does not define temperature, it tells you how to build a thermometer, which is not the same thing. It does a very good job at defining the step size over a wide range of temperatures, making sure that the marks match up everywhere according to the definition of thermodynamic temperature. But tomorrow, new technology may reveal that the ITS-90 step sizes are not the same, that the many "fixed points" are not so fixed at all. Then ITS-90 will have to be modified or abandoned. A ruler can be abandoned because it is obsolete or inaccurate but never the straight line. Thermometers like the ITS-90 can become obsolete, but never the thermodynamic temperature. PAR (talk) 12:14, 23 October 2010 (UTC)


 * Straight lines cannot be defined since it is a primitive notion, while temperature has to be defined before being put into use. Hence thermodynamic temperature doesn't enjoy the special status straight lines hold in Euclidean geometry as something that need not and can not be defined, which means it is not justified to say the "thermometer out of mercury" employs a "wrong" scale just because it isn't linear with thermodynamic temperature. If you must make an analogy, the concept here is more like the construction of the real numbers, with the zeroth law being the axioms temperature shall satisfy, and any of the scales an explicit model, which are isomorphic to each other.--Netheril96 (talk) 13:03, 23 October 2010 (UTC)


 * But to make a mercury thermometer, say you stick it in freezing water, make a mark, then boiling water, make a mark and divide the interval into 100 equal intervals. What do you do about the fact that freezing water gives slightly different marks when different people construct the thermometer? What do you do about the fact that the ideal gas law reads PV=nrX where X is a complicated function of the mercury thermometer temperature and its expansion coefficients because its expansion is not linear in terms of the thermodynamic temperature. Is that ok? PAR (talk) 14:34, 23 October 2010 (UTC)


 * The slight difference in freezing point is due to hypersensitivity in atmospheric pressure, not because it is inherently fluctuating. If you must say that is unacceptable, we can instead just set two fixed points as the triple points of water and some other predefined pure chemical substance.
 * It is true that "the ideal gas law reads PV=nrX where X is a complicated function of the mercury thermometer temperature and its expansion coefficients because its expansion is not linear in terms of the thermodynamic temperature". But that only means thermodynamic temperature is more convenient and is the reason why it is so widely used in theories. It doesn't rule out the "mercury scale" as an invalid or "wrong" scale but just puts it in a position inferior to thermodynamic scale.--Netheril96 (talk) 15:32, 23 October 2010 (UTC)


 * I'm not saying its inherently varying, only that present technology cannot measure it as reliably as the triple point. When technology advances to the point that the triple point causes problems, then we will have to have a new scale, etc. etc. Also, there is no such thing as the thermodynamic temperature scale without a physical measurement. The second law only defines thermodynamic temperature to within a scale factor. This scale factor must be defined experimentally, and that means it is never absolutely secure. But I guess this does not invalidate your point that a "mercury scale" could serve as a measure of temperature, just as a ruler with random marks on it could serve as a complicated measure of distance. I wonder if you have any references that consider such a scale as an independent scale rather than an attempt to approximate a linear thermodynamic temperature scale? I mean, I think you are correct, but I do not think anyone does it that way, nor can I think of any reason for using an "inferior" temperature scale. Also, regarding the zeroth law as providing the axioms needed for the definition of temperature, it does not. The zeroth law provides no way to order temperatures, to decide which is larger, which is smaller. Only the second law can provide this ordering. PAR (talk) 16:36, 23 October 2010 (UTC)


 * You raise that analogy to straight lines again. The straight line is a primitive notion, the genesis of everything; thermodynamic temperature is not. When measuring ideal gas, obviously "mercury scale" is clumsy, but when measuring mercury, which is clumsy? No books explicitly use that scale because they don't have to argue with you. But all my books (they are in Chinese) define temperature just as I do without mentioning order. To support my argument, I tried to find an English book stating the same thing, but up till now, I haven't succeeded even in finding a book that mentions zeroth law and most books even don't define thermodynamic temperature&mdash;they just use it.--Netheril96 (talk) 02:27, 24 October 2010 (UTC)

I agree, many books do not concern themselves with the detailed definition of temperature. But I have never heard of a book that suggests using a "mercury scale" or the output of any thermometer as anything other than an attempt to measure the thermodynamic temperature. But I am curious about what your books in Chinese say. Can you translate a statement from them that suggest the use of some other scale, like mercury, as being preferable to thermodynamic temperature?

Any definition of temperature must show that it is a real number. In the article you mentioned, construction of the real numbers, it is shown that real numbers have many relationships that must be satisfied. Not only must there be an equivalence relationship, but there must be an order relationship as well. You must have two operators defined, addition and multiplication, and their inverses, etc., etc. The zeroth law provides a small but necessary part of this. The second law provides everything else. It shows that the ratio of two thermodynamic temperatures is equal to the ratio of the work done in the cycles of a reversible engine. These work values are real numbers, and so the thermodynamic temperature is a real number. These work values have a measurable order relationship, and therefore temperature has a measurable order relationship.

I use the straight line only as an analogy, a way to explain something by using an example which is not exactly the same. No analogy is perfect, it can only be helpful, but eventually it breaks down, as you have shown. I use the analogy of the straight line because the distance on a straight line is also a real number. Distance on a straight line has many of the properties of thermodynamic temperature. It is also a helpful analogy, because there is the problem that we must try to make a ruler in the real world, an imperfect way of approximating a straight line, in order to build things, just like we must make a thermometer, an imperfect way to measure temperature, in order to build things. Your use of the mercury scale is like saying we can use a curved ruler, with marks that are not evenly spaced in order to measure distances. I agree completely, I cannot argue with that. You say that thermodynamic temperature is "superior" to the mercury scale because it is "straight" when it comes to physical theories. Again, I agree. What I am saying is that I have never heard of anyone building a ruler that was purposely curved and with unevenly spaced marks in order to accomplish the purpose of a straight, evenly marked ruler. I have never heard of anyone building a thermometer that was not an attempt to directly measure thermodynamic temperature. PAR (talk) 10:46, 24 October 2010 (UTC)


 * That's why analogy is not useful in debate because one side stresses the similarity while the other focuses on discrepancy. So we might as well drop both the straight line and construction of real numbers.
 * The words on one part (thermodynamics part) of my books are as follows (translated manually by me): If two systems contact a third system separately and their states don't change, then the two systems will be in thermal equilibrium. That is the law of thermal equilibrium, also know as the zeroth law of thermodynamics. The zeroth law of thermodynamics establishes the theoretical basis for a precise definition and measurement of temperature. According to the law, we can express the definition of temperature as: systems in thermal equilibrium have same temperature. The "third system" mentioned above can serve as a thermometer when calibrated appropriately.
 * Another part (statistical mechanics part) states:
 * $$\left(\frac{\partial\ln W_{1}\left(E_{1}\right)}{\partial E_{1}}\right)_{N_{1},V_{1},E_{1}=\bar{E_{1}}}=\left(\frac{\partial\ln W_{2}\left(E_{2}\right)}{\partial E_{2}}\right)_{N_{2},V_{2},E_{2}=\bar{E_{2}}}$$
 * The equation above is the condition for thermal equilibrium. Define
 * $$\beta(E)=\frac{1}{W}\left(\frac{\partial W}{\partial E}\right)_{N,V}=\left(\frac{\partial\ln W\left(N,V,E\right)}{\partial E}\right)_{N,V}$$
 * Then the condition for thermal equilibrium can be stated as
 * $$\beta(\bar{E_1})=\beta(\bar{E_2})$$
 * From the discussion above we can see, systems in thermal equilibrium have a common physical quantity to represent their attributes. Whenever that physical quantities of two systems equal, the systems are in thermal equilibrium. This quantity is called temperature, and the mentioned third system can be served as a thermometer. Obviously, &beta;(E) is such quantity with the same functions of temperature. Therefore in principle, we can take it as the measure of temperature for macroscopic systems. From the deduction we can also see that the value of &beta; is independent from the working material, so this is equivalent to thermodynamic scale of temperature.
 * The statistical mechanical part is illustrated in order to emphasize that in principle, $$\beta=\frac{1}{kT}$$ may serve as temperature as well, which clearly is a "curved ruler".
 * The order is not a prerequisite for a "right" scale of temperature. In fact, even thermodynamic temperature does not preserve the ordering of the quotient set of all thermal systems&mdash;a body at -1 K is hotter than that at 10000000 K.--Netheril96 (talk) 15:36, 24 October 2010 (UTC)&mdash;
 * The statistical mechanical part is illustrated in order to emphasize that in principle, $$\beta=\frac{1}{kT}$$ may serve as temperature as well, which clearly is a "curved ruler".
 * The order is not a prerequisite for a "right" scale of temperature. In fact, even thermodynamic temperature does not preserve the ordering of the quotient set of all thermal systems&mdash;a body at -1 K is hotter than that at 10000000 K.--Netheril96 (talk) 15:36, 24 October 2010 (UTC)&mdash;


 * If my analogy is not helpful to you, then I will not use it. But temperature is not analogous to a real number, it IS a real number. If you must introduce negative temperatures, you muddy the situation unnecessarily. But ok, if you must include negative temperatures, the fact still remains that heat flows from a hot body to a cold body. This provides an ordering relationship. The fact that it is not reflected by the value of temperature when negative temperatures are introduced is irrelevant. You cannot build a thermometer without being able to measure this order relationship. The zeroth law does not provide this order relationship, the second law does. The statement


 * "According to the law, we can express the definition of temperature as: systems in thermal equilibrium have same temperature."


 * is simply wrong. You cannot build a thermometer based on the zeroth law alone. You cannot simply put mercury in a tube and call it a thermometer. You must prove that the variations in its volume are a measure of temperature. You cannot do that without the second law. The second law shows that the variations in volume are a measure of temperature.


 * The equations you have written are statistical mechanics, not thermodynamics. They cannot be used to prove anything in thermodynamics, only to explain thermodynamics. Thermodynamics is the result of actual measurements. It cannot be disproven, except to within experimental error. Statistical mechanics is not the result of measurement. If statistical mechanics disagrees with thermodynamics, then statistical mechanics is wrong. The only reason statistical mechanics is "valid" is because it predicts the results of thermodynamics. It also predicts results that are outside of thermodynamics, which lends further support to its validity.


 * I agree that B=1/kT is a valid measure of thermodynamic temperature and that it constitutes a "curved ruler" with respect to T, but the second law says that the measured work ratio qh/qc=Th/Tc and now it reads qh/qc=Bc/Bh, so the ratio is still a ratio of heats from a reversible engine, independent of the material used in the engine, rather than a function of mercury expansion coefficients, or any material property. Point taken. I would have no problem using B as a measure of thermodynamic temperature, and calling it the "straight line". But your mercury thermometer will suffer - expansion is roughly linear in thermodynamic T, not thermodynamic B, so marking off equal divisions between 1/273.15 and 1/373.15 (0 and 100 C) on a mercury thermometer will give a much worse measure of thermodynamic B than if you used that method to measure thermodynamic T. PAR (talk) 19:08, 24 October 2010 (UTC)


 * I agree that the book is wrong, but for different reason. The article states: "then one can construct an injective function ƒ: M → R, by which every thermal system will have a number associated with it such that when and only when two thermal systems have same such value, they will be in thermal equilibrium.", which means not only that systems in thermal equilibrium have same temperature, but also that systems at same temperature shall be in thermal equilibrium. This does not involve second law, and by this definition it is easy to construct the order relationship you require&mdash;for any valid scale, since &fnof; is injective, there is a bijective function g such that &beta;=g(X). Then you can just define the order as if $$g(X_1)<g(X_2)$$ then 1 is hotter than 2. You may go even further to construct other structures like a metric, but all those are just additives to temperature itself, rather than what make temperature temperature. In other words, you first define the set of temperature, then you define an order relationship which satisfies the second law upon it.--Netheril96 (talk) 10:11, 25 October 2010 (UTC)


 * Ok, but the second law does more than just establish an order relationship, it shows that temperature is represented by a real number, with all that that implies. The contribution of the second law in describing the nature of temperature is vital, even if it is just an additive. The only thermometer you can build using the zeroth law is one that answers "yes" or "no" to the question of whether two systems are in equilibrium. Only with the second law can you build a thermometer that answers the question "which is hotter?" - i.e. the order relationship. Furthermore, only with the second law can you come up with the real number known as thermodynamic temperature (to within a scale factor). PAR (talk) 21:28, 25 October 2010 (UTC)


 * So what about ideal gas scale and the "&beta;" scale mentioned above? Both of them are not defined in terms of second law, although they can be proved by second law to be strongly related to T. And I don't know what is your logic on "The contribution of the second law in describing the nature of temperature is vital, even if it is just an additive". Why an additive is vital in definition? It's an indispensable part of its nature, but that should be addressed in articles about temperature's property, along with things like an indication of mean translational energy, not in its definition.--Netheril96 (talk) 01:46, 26 October 2010 (UTC)

The "β" scale is defined in terms of the second law. The second law specifies how to measure the ratio of two temperatures, not the temperature itself. Therefore it specifies how to measure the ratio of two "β"'s. "β" scale is special: If we say that thermodynamic temperature T is the simplest scale, "β" is the only scale about which we can say the same.

The ideal gas law is defined in terms of the second law, since it is defined in terms of thermodynamic temperature, and the full nature of thermodynamic temperature is defined in terms of the second law. Another way of looking at it is to define an ideal gas in terms independent of temperature, and then show that PV is proportional to T. For example, you can specify an ideal gas as one in which the ratio of heats in the power cycles of a reversible engine is equal to the ratio of PV's for the gas. It follows that the ratio of PV's are equal to the ratio of temperatures.

Regarding the use of the word "additive", this is a semantic argument. It doesn't matter what definitions you use to describe how things work, as long as we agree on how things work. I don't want to argue about whether the zeroth law is fundamental and the second law additive when it comes to temperature, or whether both are fundamental. This is an argument over the meaning of the word "fundamental" and I don't care about that, all I care about is how things work. As you say, the second law provides an indispensable part of the nature of temperature. Ok, good. This is an article about temperature scales. The role of the second law in defining a useful temperature scale is indispensable. Ok, good.

The bottom line is that a definition of temperature must imply the construction of a thermometer. The zeroth law alone does not tell you the properties of a thermometer, it does not provide for the ordering of temperatures. The ordering of temperatures is an indispensable part of the nature of temperature. I don't want to argue over whether it is "fundamental" to the definition of temperature.


 * For what do you reason that &beta; scale and ideal gas scale are based on the second law?--Netheril96 (talk) 13:12, 26 October 2010 (UTC)


 * &beta;=1/kT where T is thermodynamic temperature. Thermodynamic temperature is based on the second law. (and zeroth). For an ideal gas, PV=nRT where T is the thermodynamic temperature, which requires the second law for its definition. How can you define an ideal gas scale without the second law? PAR (talk) 16:11, 26 October 2010 (UTC)


 * Your logic confuses me. According to you, &beta;=1/kT so &beta; is derived from T; so why can't I say because T=1/k&beta; then T is based on &beta;?--Netheril96 (talk) 09:17, 28 October 2010 (UTC)


 * Yes, T is based on &beta; is acceptable. I think the confusion is between the thermodynamic, measurable T and &beta; and the statistical mechanics interpretation of the measured quantities. Thermodynamics is based on actual measurements, statistical mechanics is not. (unless perhaps it is attempting to explain a phenomenon outside of thermodynamics). Statistical mechanics explains the results of thermodynamic measurements. It explains thermodynamics, it does not replace it. Certain quantities and concepts in statistical mechanics are seen to correspond to measurable thermodynamic quantities, such as the energy per translational degree of freedom (stat mech) and the thermodynamic temperature (thermodynamics). When I said &beta; is derived from T, I just meant that if you give me a value of T, I will give you a value of &beta; by calculating 1/kT. If you wish to define &beta; as a purely statistical mechanical variable, then the fact that it is equivalent to 1/kT where T is the thermodynamic temperature is just an example of statistical mechanics success at explaining thermodynamics. If &beta; is a purely statistical mechanical concept, then there can be no thermometer that measures &beta; Only when you make &beta; a thermodynamic variable, equal to 1/kT, a measurable quantity, can you make a &beta; thermometer and have a &beta; scale. PAR (talk) 11:56, 28 October 2010 (UTC)

Fermi's book
Fermi's book really is not such a great book anymore as it was written I believe before even the zeroth law was formulated. If you are trying to argue against the Zeroth law definition of temperature you ought to use a more modern treatise or else being obsolete in your statements by default. Kbrose (talk) 04:31, 26 October 2010 (UTC)


 * I agree, Fermi's book makes no mention of the zeroth law, but I was not recommending it to dispute the zeroth law, only to show the contribution of the second law to the definition of temperature. The zeroth law provides an equivalence relationship, which means you can form a "quotient set", as Netheril96 puts it. An element of the set is the set of all systems in thermodynamic equilibrium with each other, and any system from one element will not be in equilibrium with any system from another element of the set. The next step is to say that the temperature of each system in a given element is the same. And that is as far as you can go. The zeroth law provides no ordering of these elements, no notion of "this system is hotter than that system". In other words, it does not fully define temperature as we know it. The second law provides the rest of the notions of temperature. The second law tells you which system is hotter, which is colder. Even more, it assigns a real number to thermodynamic temperature, to within a scaling factor. Fermi's book outlines the procedure by which the second law does this. It comes closer than most books to building up thermodynamics from scratch. It also draws a clear distinction between thermodynamics and statistical mechanics. It never uses a statistical mechanical argument to prove a thermodynamic result. It only uses statistical mechanics to give intuitive meaning and insight into thermodynamic results. These two things put it above many other books. PAR (talk) 12:34, 26 October 2010 (UTC)
 * You continue to use an outdated reference to support your opinion about the zeroth law, that the reference does not consider, despite agreeing to that point. Therefore by default, all your logic in support of 2nd law explanation, and against 0th law, is void.