A Macroscopic Definition of Matter

A Macroscopic Definition of Matter 18.1 Solids, Liquids, and Gases Each of the elements and most compounds can exist as a solid, liquid, or gas - the three most common phases of matter The change between liquid and solid (freezing or melting) or between liquid and gas (boiling or condensing) is called a phase change Solid: A solid is a rigid macroscopic system consisting of particle-like atoms connected by spring-like molecular bonds Liquid: A liquid is a system in which the molecules are loosely held together by weak molecular bonds Gas: A gas is a system in which each molecule moves through space as a free, non interacting particle until, on occasion, it collides with another molecule or with the wall of the container State variables The parameters used to characterize or describe a macroscopic system are known as state variables because, taken all together, they describe the state of the macroscopic system A system is said to be in thermal equilibrium if its state variables are constant and not changing 18.2 Atoms and Moles The mass of a microscope system is directly related to the total number of atoms or molecules in the system, denoted N The symbol ~, if you are not familiar with it, stands for "has the order of magnitude". It means that the number is known only to within a factor of 10 or so It is often useful to know the number of atoms or molecules per cubic meter in a system. We call this quantity the number density. It characterizes how densely the atoms are packed together within the system The value of N/V in a uniform system is independent of the volume V. That is, the number density is the same whether you look at the whole system or just a portion of it Important equations: N V (number density) NA = 6:02 £ 1023 (Avogadro’s number) n= N NA N= (moles of substance) M (molar mass) m Atomic mass and atomic number The sum of the number of protons and neutrons is called the atomic mass number A: A = number of protons + number of neutrons For our purposes, it will be sufficient to overlook the slight difference and use the integer atomic mass numbers as the values of the atomic mass For molecules, the molecular mass is the sum of the atomic masses of the atoms forming the molecule Moles and Molar Mass By definition, one mole of matter, be it solid, liquid, or gas, is the amount of substance containing as many basic particles as there are atoms in 0.012 kg (12g) of carbon 12 Helium is a monoatomic gas, meaning that the basic particle is the helium atom. But oxygen gas is a diatomic gas because the basic particle is the two-atom diatomic molecule O2 For other substances, whose atomic or molecular masses are given relative to C 12, the numerical value of the molar mass is the numerical value of the atomic or molecular mass divided by 1000 18.3 Temperature Temperature (T) is related to a systems thermal energy. Thermal energy is the kinetic and potential energy of the atoms and molecules in a system as they vibrate (a solid) or move around (a gas). A system has more thermal energy when it is "hot" than when it is "cold" A thermometer can be any small macroscopic system that undergoes a measurable change as it exchanges thermal energy with its surroundings In a common glass-tube thermometer, for example, a small volume of mercury or alcohol expands or contracts when placed in contact with a "hot" or "cold" object Absolute zero and absolute temperature In practice, the most useful thermometers have a physical property that changes linearly with temperature The constant-volume gas thermometer depends on the fact that the absolute pressure (not the gauge pressure) of a gas in a sealed container increases linearly as the temperature increases The pressure in a gas is due to collisions of the molecules with each other and the walls of the container. A pressure of zero would mean that all motion, and thus all collisions, had ceased The temperature at which all motion would cease, and at which thermal energy is zero, is called absolute zero On the kelvin scale, the absolute zero is 0 K, the freezing point of water is 273 K, and the boiling point of water is 373 K 18.4 Thermal Expansion Objects expand when heated. This thermal expansion is why the liquid rises in a thermometer and why pipe, highways, and bridges have expansion joints For most solids, the fractional change in length, delta L/L, is proportional to the temperature change with a proportionality coefficient that depends on the material Where alpha is the materials coefficient of linear expansion ¢L L = ®¢T Volume expansion is treated the same way. If an objects volume changes during a temperature change, the fractional change in volume is... Where beta is the materials coefficient of volume expansion ¢V = ¯¢T V Liquids are constrained by the shape of their container, so liquids are characterized by a volumeexpansion coefficient but not by A linear-expansion coefficient Solids expand linearly in all three directions and in the process a solid changes its volume That is, the fractional change in volume is three times the fractional change in the length of the sides If you lower the temperature of water, its volume contracts as expected. But only until the temperature reaches 4 degrees Celsius. If you continue cooling water, from 4 degrees Celsius down to the freezing point at 0 degrees, the volume expands 18.5 Phase Changes Even though a system is being heated, the liquid water temperature doesn't begin to rise until an the ice has melted If you were to turn the flame off at any point, the system would remain a mixture of ice and liquid water at 0 degrees Celsius The thermal energy of a solid is the kinetic energy of the vibrating atoms plus the potential energy of the stretched and compressed molecular bonds The temperature at which a solid becomes a liquid or, if the thermal energy is reduced, a liquid becomes a solid is called the melting point or the freezing point A system at the melting point is in phase equilibrium, meaning that any amount of solid can coexist with any amount of liquid The temperature at which a gas becomes a liquid or, if the thermal energy is increased, a liquid becomes a gas is called the condensation point or the boiling point Phase diagrams A phase diagram is used to show how the phases and phase changes of a substance vary with both temperature and pressure Crossing the solid-liquid boundary corresponds to melting or freezing while crossing the liquid-gas boundary corresponds to boiling or corresponding There's another possibility - crossing the solid-gas boundary. The phase change in which a solid becomes a gas is called sublimation Water is a very unusual substance in that the density of ice is less than the density of liquid water. That is why ice floats The liquid-gas boundary ends at a point called the critical point. Below the critical point, liquid and gas are clearly distinct and there is a phase change if you go from one to the other. But there is no clear distinction between liquid and gas at pressures or temperatures above the critical point The final point of interest on the phase diagram is the triple point where the phase boundaries meet. The triple point is the one value of temperature and pressure for which all three phases can coexist in phase equilibrium The triple-point temperature of water is an ideal reference point, hence the Kelvin temperature scale is defined to be a linear temperature scale starting from 0 K at absolute zero and passing through 273.16 K at the triple point of water 18.6 Ideal Gases This is a model of an atom - what we might call the ideal atom - because it ignores the weak attractive interactions that hold liquids and solids together An ideal gas is a gas of small, hard, randomly moving atoms that bounce off each other and the walls of their container but otherwise do not interact The ideal gas is a somewhat simplified description of a real gas, but experiments show that the ideal-gas model is quite good for real gases if two conditions are met: (1) the density is low (i.e., the atoms occupy a volume much smaller than that of the container), and (2) the temperature is well above the condensation point If the density gets too high, or the temperature too low, then the attractive forces between the atoms begin to play an important role and our model, which ignores those attractive forces, falls As far as translational motion is concerned, the ideal-gas model does not distinguish between a monatomic gas and a diatomic gas; both are considered as simply small, hard spheres The Ideal-Gas Law The state variables for an ideal gas are the volume V of its container, the number of moles n of the gas present in the container, the temperature T of the gas and its container, and the pressure p that the gas exerts on the walls of the container (Ideal gas law) pV = nRT The ideal-gas law is a relationship among the four state variables - p, V, n, and T - that characterize a gas in thermal equilibrium The surprising fact, and one worth commenting upon, is that all gases have the same graph and same value of R pf V f pi V i = Tf Ti pV = N kBT (Ideal gas in a sealed container) (Ideal-gas law) 18.7 Ideal-Gas Processes If the state variables change, as they would from heating or compressing the gas, the state of the gas changes. An ideal-gas process is the means by which the gas changes from one state to another The pV Diagram The important idea behind the pV diagram is that each point on the graph represents a single, unique state of the gas. That seems surprising at first, because a point on the graph only directly specifies the values of p and V But knowing p and V, and assuming that n is known for a sealed container, we can find the temperature by using the ideal-gas law. Thus each point actually represents a triplet of values (p, V, T) specifying the state of the gas An ideal-gas process is a "trajectory" in the pV diagram showing all the intermediate states through which the gas passes Although the initial and final states are the same for each of them, the particular process by which the gas changes - that is, the particular trajectory - will turn out to have very real consequences Quasi-Static Processes Strictly speaking, the ideal-gas law applies only to gases in thermal equilibrium, meaning that the state variables are constant and not changing To use the ideal-gas law throughout, we will assume that the process occurs so slowly that the system is never far from equilibrium. A process that is essentially in thermal equilibrium at all times is called a quasi-static process Constant-Volume Process Many important gas processes take place in a container of constant, unchanging volume. A constantvolume process is called an isochoric process, where iso is a prefix meaning "constant" or "equal" while choric is from a Greek root meaning "volume" Any isochoric process appears on a pV diagram as a vertical line Constant-Pressure Process Other gas processes take place at a constant, unchanging pressure. A constant-pressure process is called an isobaric process, where baric is from the same root as "barometer" and means "pressure" In other words, the gas pressure is determined by the requirement that the gas must support both the mass of the piston and the air pressing inward This pressure is independent of the temperature of the gas or the height of the piston, so it stays constant as long as M is unchanged If the cylinder is warmed, the gas will expand and push the piston up. We call this an isobar expansion. An isobaric compression occurs if the gas is cooled, lowering the piston. Any isobaric process appears on a pV diagram as a horizontal line Constant-Temperature Process If the piston is pushed slowly, then heat energy transfer through the walls of the cylinder keeps the gas at the same temperature as the surrounding liquid. This is an isothermal compression. The reverse process, with the piston slowly pulled out, would be an isothermal expansion The inverse relationship between p and V causes the graph of an isothermal process to be a hyperbola A lower-temperature process is represented by a hyperbola closer to the origin than a highertemperature process