# Getting Acquainted with Entropy

You can experience directly the massA measure of the force required to impart unit acceleration to an object; mass is proportional to chemical amount, which represents the quantity of matter in an object., volume, or temperatureA physical property that indicates whether one object can transfer thermal energy to another object. of a substanceA material that is either an element or that has a fixed ratio of elements in its chemical formula., but you cannot experience its entropyA thermodynamic state function, symbol S, that equals the reversible heat energy transfer divided by temperature; higher entropy corresponds to greater dispersal of energy on the molecular scale. See also standard entropy.. Consequently you may have the feeling that entropy is somehow less real than other properties of matterAnything that occupies space and has mass; contrasted with energy.. We hope to show in this section that it is quite easy to predict whether the entropy under one set of circumstances will be larger than under another set of circumstances, and also to explain why. With a little practice in making such predictions in simple cases you will acquire an intuitive feel for entropy and it will lose its air of mystery.

The entropy of a substance depends on two things: first, the *state* of a substance—its temperature, pressureForce per unit area; in gases arising from the force exerted by collisions of gas molecules with the wall of the container., and amount; and second, how the substance is *structured* at the molecular level. We will discuss how *state* properties affect entropy first.

**Temperature** As we saw in the last section, there should be only one way of arranging the energyA system's capacity to do work. in a perfect crystalA solid with a regular polyhedral shape; for example, in sodium chloride (table salt) the crystal faces are all at 90° angles. A solid in which the atoms, molecules, or ions are arranged in a regular, repeating lattice structure. at 0 K. If *W* = 1, then *S* = *k* ln *W* = 0; so that the *entropy should be zero at the absolute zeroThe minimum possible temperature: 0 K, -273.15 °C, -459.67 °F. of temperature*. This rule, known as the **third law of thermodynamicsA formal statement that at the absolute zero of temperature the value of the entropy of a perfect crystal is equal to zero.**, is obeyed by all solids unless some randomness of arrangement is accidentally “frozen” into the crystal. As energy is fed into the crystal with increasing temperature, we find that an increasing number of alternative ways of dividing the energy between the atomsThe smallest particle of an element that can be involved in chemical combination with another element; an atom consists of protons and neutrons in a tiny, very dense nucleus, surrounded by electrons, which occupy most of its volume. become possible. *W* increases, and so does *S*. Without exception the entropy of any pure substance *always increases with temperature*.

**Volume and Pressure** We argued earlier that when a gasA state of matter in which a substance occupies the full volume of its container and changes shape to match the shape of the container. In a gas the distance between particles is much greater than the diameters of the particles themselves; hence the distances between particles can change as necessary so that the matter uniformly occupies its container. doubles its volume, the number of ways in which the gas molecules can distribute themselves in space is enormously increased and the entropy increases by 5.76 J K^{–1}. More generally the entropy of a gas always *increases with increasing volume* and *decreases with increasing pressure*. In the case of solids and liquids the volume changes very little with the pressure and so the entropy also changes very little.

**Amount of Substance** One of the main reasons why the entropy is such a convenient quantity to use is that its magnitude is *proportional to the amount of substance*. Thus the entropy of 2 mol of a given substance is twice as large as the entropy of 1 mol. Properties which behave in this way are said to be **extensive properties**. The mass, the volume, and the enthalpyA thermodynamic state function, symbol H, that equals internal energy plus pressure x volume; the change in enthalpy corresponds to the energy transferred as a result of a temperature difference (heat transfer) when a reaction occurs at constant pressure. are also extensive properties, but the temperature, pressure, and thermodynamic probability are not.

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