Kinetic Molecular Theory Basic Concepts
The gas laws developed by Boyle, Charles, and Gay-Lussac are based upon empirical observations and describe the behavior of a gas in macroscopic terms, that is, in terms of properties that a person can directly observe and experience. An alternative approach to understanding the behavior of a gas is to begin with the atomic theory, which states that all substances are composed of a large number of very small particles (molecules or atoms). In principle, the observable properties of gas (pressure, volume, temperature) are the consequence of the actions of the molecules making up the gas.
The Kinetic Molecular Theory of Gases begins with five postulates that describe the behavior of molecules in a gas. These postulates are based upon some simple, basic scientific notions, but they also involve some simplying assumptions. In reading a postulate, do two things. First, try to understand and appreciate the basic physical idea embodied in the postulate; this idea will ultimately be important in understanding the macroscopic properties of the gas in terms of the behavior the microscopic molecules making up the gas. Second, identify possible weakness or flaws in the postulates. Inaccurate predictions by a theory derive from flawed postulates used in the derivation of the theory.
thermodynamic process is a passage of a thermodynamic system from an initial state to a final state. In equilibrium thermodynamics, the initial and final states are states of internal thermodynamic equilibrium, each respectively fully specified by a suitable set of thermodynamic state variables, that depend only on the current state of the system, not the path taken to reach that state. In general, in a thermodynamic process, the system passes through physical states which are not describable as thermodynamic states, because they are far from internal thermodynamic equilibrium. It is possible, however, that a process may take place slowly or smoothly enough to allow its description to be usefully approximated by a continuous path of thermodynamic states. Then it may be approximately described by a process function that does depend on the path.
Thermodynamic parameters
The central concept of thermodynamics is that of energy, the ability to do work. As stipulated by the first law, the total energy of the system and its surroundings is conserved. External energy may be transferred into a body—increasing its internal energy—by heating, compression, or addition of matter, and extracted from a body—decreasing its internal energy—either by cooling, expansion, or extraction of matter.
For comparison, in mechanics, energy transfer results from a force which causes displacement, the product of the two being the amount of energy transferred. In a similar way, thermodynamic systems can be thought of as transferring energy as the result of a generalized force causing a generalized displacement, with the product of the two being the amount of energy transferred. The most direct example is the work term PdV, where pressure P (force per area) plays the role of generalized force and infinitesimal change of volume dV plays the role of displacement (dV can, indeed, be effected by the infinitesimal displacement of a wall of a container).
These thermodynamic "force-displacement" pairs are known as conjugate variables. The most common conjugate thermodynamic variables are pressure-volume (mechanical parameters), temperature-entropy (thermal parameters), and chemical potential-number of moles (material parameters). A conjugate pair always consists of an intensive (size independent) parameter (pressure, temperature, chemical potential) and an extensive (linear in size) parameter (volume, entropy, number of moles). Two further examples of conjugate pairs are magnetic field-magnetization and electric field-polarization.
Thermodynamic equilibrium is an axiomatic concept of classical thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by permeable walls. In thermodynamic equilibrium there are no net macroscopic flows of matter or of energy, either within a system or between systems. In a system in its own state of internal thermodynamic equilibrium, no macroscopic change occurs. Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal, mechanical, chemical, and radiative equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a thermodynamic operation. In a macroscopic equilibrium, almost or perfectly, exactly balanced microscopic exchanges occur; this is part of the notion of macroscopic equilibrium.
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with thermodynamic systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium; for they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems and to chemical reactions. Non-equilibrium thermodynamics is concerned with transport processes and with the rates of chemical reactions.[1] Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.
29.
The kinetic theory of gases describes a gas as a large number of small particles (atoms or molecules), all of which are in constant, random motion. The rapidly moving particles constantly collide with each other and with the walls of the container. Kinetic theory explains macroscopic properties of gases, such as pressure, temperature, viscosity, thermal conductivity, and volume, by considering their molecular composition and motion. The theory posits that gas pressure is due to the impacts, on the walls of a container, of molecules or atoms moving at different velocities.
Kinetic theory defines temperature in its own way, not identical with the thermodynamic definition.[1]
Perfect gas, also called ideal gas, a gas that conforms, in physical behaviour, to a particular, idealized relation between pressure, volume, and temperature called thegeneral gas law. This law is a generalization containing both Boyle’s law andCharles’s law as special cases and states that for a specified quantity of gas, the product of the volume v and pressure p is proportional to the absolute temperaturet; i.e., in equation form, pv = kt, in which k is a constant. Such a relation for a substance is called its equation of state and is sufficient to describe its gross behaviour.
The general gas law can be derived from the kinetic theory of gases and relies on the assumptions that (1) the gas consists of a large number of molecules, which are in random motion and obey Newton’s laws of motion; (2) the volume of the molecules is negligibly small compared to the volume occupied by the gas; and (3) no forces act on the molecules except during elastic collisions of negligible duration.
Although no gas has these properties, the behaviour of real gases is described quite closely by the general gas law at sufficiently high temperatures and low pressures, when relatively large distances between molecules and their high speeds overcome any interaction. A gas does not obey the equation when conditions are such that the gas, or any of the component gases in a mixture, is near its condensation point, the temperature at which it liquefies.
The general gas law may be written in a form applicable to any gas, according toAvogadro’s law, if the constant specifying the quantity of gas is expressed in terms of the number of molecules of gas. This is done by using as the mass unit the gram-mole; i.e., the molecular weight expressed in grams. The equation of state of n gram-moles of a perfect gas can then be written as pv/t = nR, in which R is called the universal gas constant. This constant has been measured for various gases under nearly ideal conditions of high temperatures and low pressures, and it is found to have the same value for all gases: R = 8.314472 joules per mole-kelvin.
30.
The Kinetic Theory of Gases
We can summarize the kinetic theory of gases with four basic postulates:
Gases are made up of molecules: We can treat molecules as point masses that are perfect spheres. Molecules in a gas are very far apart, so that the space between each individual molecule is many orders of magnitude greater than the diameter of the molecule.
Molecules are in constant random motion: There is no general pattern governing either the magnitude or direction of the velocity of the molecules in a gas. At any given time, molecules are moving in many different directions at many different speeds.
The movement of molecules is governed by Newton’s Laws: In accordance with Newton’s First Law, each molecule moves in a straight line at a steady velocity, not interacting with any of the other molecules except in a collision. In a collision, molecules exert equal and opposite forces on one another.
Molecular collisions are perfectly elastic: Molecules do not lose any kinetic energy when they collide with one another.
The kinetic theory projects a picture of gases as tiny balls that bounce off one another whenever they come into contact. This is, of course, only an approximation, but it turns out to be a remarkably accurate approximation for how gases behave in the real world.
These assumptions allow us to build definitions of temperature and pressure that are based on the mass movement of molecules.