Mixtures of gases could undergo chemical reactions. More complicated: it might have different phases (solid, liquid, gas) and Of them define the state (for a given mass of gas), but all four have useful This means an ideal gas has four state variables, or Its value everywhere, that is, for any equilibrium state. So knowing S ( P 1, V 1 ) at a single point in the plane, we can find Where the integral is understood to be along any reversible path -they all We can therefore define a new state variable, S , called the entropy, such that the difference Where the i labels intermediate isothermal changes. ∑ a c Q i T i = ∫ a c d Q / T is the s a m e for all reversible paths We can just apply our “cutting a corner” argument again and Of little bits of isotherms and adiabats. In fact, any path you can draw in the planeįrom a to c can be approximated arbitrarily well by a reversible route made up In other words, any reversible route, can be constructed by adding littleĬarnot cycles to the original route. Evidently, then,īut we can now cut corners on the corners: any zigzag routeįrom a to c , with the zigs isotherms and the zags adiabats, Notice that e f g d is a little Carnot cycle. Path a e f g c instead of a d c , where e f is an isotherm and f g an adiabat. Let’s begin by cutting a corner in the previous route: Of course, we’ve chosen two particular reversible routesįrom a to c : each is one stretch of isotherm and one of The ratio of the heat supplied to the temperature at which is was However, notice that one thing (besides total internal But Something Heat Related is the Same: Introducing Entropy Gas, but with more heat and less work along the top route. Supplied heat, and the two different routes from a to c have the same total energy supplied to the It does of course have a definite internalĮnergy, but that energy can be increased by adding a mix of external work and So we cannot say that a gas at a given ( P, V ) contains a definite amount of heat. The same place, but with quite a different This is a perfectly well defined reversible route, ending at Why not?īecause we could equally well have gone from a to c by a route which is the second half of the Two points with the first half of a Carnot cycle, from a to c :Įvidently, heat Q H has been supplied to the gas -but thisĪt ( P c, V c ) has Q H more heat than the gas at ( P a, V a ). Gas from one point in the ( P, V ) plane to another, and begin by connecting the To make this explicit, instead of cycling, let’s track the In other words, the total amount of “heat” inĪbout how much heat there is in the gas is meaningless. Himself thought that something else besides total energy was conserved: theīut we know better: in a Carnot cycle, the heat leaving the gas on theĮntering earlier, by just the amount of work performed. Of the gas is the same at the end of the cycle as it was at the beginning, but We know, of course, one thing that doesn’t change: the internal energy To get a clue about what stays the same in a reversibleĬycle, let’s review the Carnot cycle once more. Heat Changes along Different Paths from a to c Labeled entropy that doesn’t change in a reversible process, but always Parameter? The answer turns out to be yes: there is a parameter Clausius The “amount of irreversibility” to be measured? Does it correspond to some thermodynamic Reversible engine has to equal that of the Carnot cycle, and any nonreversible The second law, that heat only flows from a warmer body to aĬolder one, does have quantitative consequences: the efficiency of any Other names, but those are merely notational developments.) Work, the unit wasn’t called a Joule, and the different types of energy had Up to get the total and that will remain constant. Heat units and energy units, calories to joules, since all the other types ofĮnergy (kinetic, potential, electrical, etc.) are already in joules, add it all His aim was to express both laws in aĬonservation of total energy including heat energy -is easy toĮxpress quantitatively: one only needs to find the equivalence factor between So what, exactly, is entropy, where did this word comeĬlausius in 1865, a few years after he stated the laws of thermodynamics This was called the Heat Death of the Universe, and may still be what’sīelieved, except that now everything will also be flying further and further Used to describe the approach to an imagined final state of the universe whenĮverything reaches the same temperature: the entropy is supposed to increase toĪ maximum, then nothing will ever happen again. Synonym for chaos, for example: the entropy in my room increases as the The word “entropy” is sometimes used in everyday life as a Previous index next A New Thermodynamic Variable: Entropy
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