Simple Nature - Light and Matter

But physics deals with operational definitions, i.e., definitions ofhow to measure the thing in question. How do we measure temperature?One common feature of all temperature-measuring devicesis that they must be left for a while in contact with the thing whosetemperature is being measured. When you take your temperaturewith a fever thermometer, you are waiting for the mercury inside tocome up to the same temperature as your body. The thermometeractually tells you the temperature of its own working fluid (in thiscase the mercury). In general, the idea of temperature depends onthe concept of thermal equilibrium. When you mix cold eggs fromthe refrigerator with flour that has been at room temperature, theyrapidly reach a compromise temperature. What determines thiscompromise temperature is conservation of energy, and the amountof energy required to heat or cool each substance by one degree.But without even having constructed a temperature scale, we cansee that the important point is the phenomenon of thermal equilibriumitself: two objects left in contact will approach the sametemperature. We also assume that if object A is at the same temperatureas object B, and B is at the same temperature as C, thenA is at the same temperature as C. This statement is sometimesknown as the zeroth law of thermodynamics, so called because afterthe first, second, and third laws had been developed, it was realizedthat there was another law that was even more fundamental.Thermal expansionThe familiar mercury thermometer operates on the principle thatthe mercury, its working fluid, expands when heated and contractswhen cooled. In general, all substances expand and contract withchanges in temperature. The zeroth law of thermodynamics guaranteesthat we can construct a comparative scale of temperaturesthat is independent of what type of thermometer we use. If a thermometergives a certain reading when it’s in thermal equilibriumwith object A, and also gives the same reading for object B, thenA and B must be the same temperature, regardless of the details ofhow the thermometers works.What about constructing a temperature scale in which everydegree represents an equal step in temperature? The Celsius scalehas 0 as the freezing point of water and 100 as its boiling point. Thehidden assumption behind all this is that since two points define aline, any two thermometers that agree at two points must agree atall other points. In reality if we calibrate a mercury thermometerand an alcohol thermometer in this way, we will find that a graphof one thermometer’s reading versus the other is not a perfectlystraight y = x line. The subtle inconsistency becomes a drastic onewhen we try to extend the temperature scale through the pointswhere mercury and alcohol boil or freeze. Gases, however, are muchmore consistent among themselves in their thermal expansion thanf / Thermal equilibrium canbe prevented. Otters have a coatof fur that traps air bubbles for insulation.If a swimming otter wasin thermal equilibrium with coldwater, it would be dead. Heat isstill conducted from the otter’sbody to the water, but muchmore slowly than it would be in awarm-blooded animal that didn’thave this special adaptation.g / A hot air balloon is inflated.Because of thermal expansion,the hot air is less dense thanthe surrounding cold air, andtherefore floats as the cold airdrops underneath it and pushes itup out of the way.Section 5.1 Pressure and Temperature 303