CHAPTER 1 LECTURE NOTES System, Surroundings, and States Fig. 1.4 Note the three different types of systems based on the type of boundary between system and surroundings. Intensive and Extensive Properties Intensive Properties: Intrinsic to the substance, does not change with the amount of substance. Examples: density, molecular mass, refractive index Extensive Properties: Depend on the amount of substance. Examples: mass, volume, energy State Variables: The minimum number of properties that need to be specified (i.e., measured) in order to determine the state of the system. Equilibrium: A system is in equilibrium with its surroundings when its state variables do not change with time. Thermal Equilibrium: When two bodies are in contact and their temperature remain constant, they are in thermal equilibrium. Two bodies in thermal equilibrium with a third are also in thermal equilibrium with each other. Temperature scales Celsius &amp; Farenheit: Both based on the freezing point and boiling point of water at 1 atm pressure. Kelvin Scale: Based on ideal gas behavior extrapolated to absolute zero. Triple point scale: Based on a single point: the triple point of water, which is defined to be exactly 273.16 K. Pressure Pressure is force per unit area. The most common units in the US for pressure of gases are the atmosphere (atm), or pounds per square inch (psi). Another common unit is torr or mm Hg, which refers to the height of a mercury column supported by the pressure of the gas. 1 atm = 760 torr = 760 mm Hg. The SI unit of pressure is the Pascal (Pa). 1 Pa = 1 N m 2. A more useful unit when dealing with gases is the bar. 1 bar = 105 Pa. 1 bar is close to, but not the same as 1 atm. 1 atm = 1.01325 bar = 101.325 kPa = 101,325 Pa = 760 torr. 1 bar = 100.000 kPa = 100,000 Pa = 750 torr. Ideal Gas Law Pressure measuring devices: A mercury barometer is commonly used to measure atmospheric pressure. A mercury manometer is commonly used to measure pressure of gases in various containers. There are two types of manometers: closed end and open end. See Fig. 1.4 and note how they work. See Example 1.1, Problems 1.7 1.9 Boyle s Law: PV = constant, at constant T. Lines connecting points on a PV diagram at a fixed temperature are called isotherms. Charles (Gay Lussac s) Law: V/T = constant, at constant P. Ideal Gas Law: Combination of Boyle s and Charle s Laws: PV/T = constant. PV = nRT Ideal Gas Law(alternate statement): R is the Universal Gas Constant. Its numerical value in various systems of units is given in Table 1.1, on p. 16. Problems: 1.11 1.13 Molecular masses from Ideal Gas Law: PV = nRT = M RT P= Therefore, m m RT n RT V RT = ( V ) M = G M , where is the density of the gas. RT . M=G P Also see Problems 1.15 1.17 Important Results from Kinetic Theory Pressure: PV = 1 Nmu 2 . 3 The quantity u 2 is called mean-square velocity. Kinetic Energy: (1.41) A k = 1 mu 2 = 3 k B T per molecule, where kB is called the Boltzmann constant. 2 2 E k = 3 RT, per mole. 2 Therefore, R = LkB, where L is the Avogradro number. Graham s Law of Effusion: Rate of effusion is inversely proportional to the molecular mass. Assumptions of Kinetic Theory: Gases consist of particles which are so small compared to the distances between them that the volume of the individual particles can be assumed to be zero. The particles are in constant motion, colliding with each other and the walls of the container in perfectly elastic collisions. Collisions with the walls give rise to the pressure exerted by the gas. The particles have no forces of attraction or repulsion with each other or the walls of the container. The average kinetic energy of a collection of gas particles is directly proportional to the Kelvin temperature. Real Gases Real gases deviate from ideal behavior because they do not strictly conform to the assumptions listed above. The compression factor, Z, defined as PV m PV Z = nRT = RT , (1.98) Vm is the molar volume, is useful to analyze the deviation from ideal behavior. For ideal gas, Z = 1 always. See Fig. 1.17 (p. 33). Real gases have forces of attraction between molecules. Therefore, if the temperature is low enough, application of pressure will lead to the formation of molecular clusters. The clusters grow into liquid droplets. This is the principle of liquefaction of gases by application of pressure and cooling. If gases behaved ideally, they would never form liquids. There is a special temperature, called critical temperature, Tc, beyond which gases cannot be liquefied by application of pressure. See Fig. 1.18. At Tc, there is a certain value of P and V at which the PV curve goes through an inflection. This is called the critical point. The pressure and volume at this point are called the critical pressure, Pc ,and critical volume, Vc , respectively. The Below Tc, there is a region where the gas and liquid are in equilibrium. The <a href="/keyword/van-der-waals-equation/" >van der waals equation</a> : Corrects for two assumptions inherent in Ideal Gas Law: (a) attraction/repulsion between molecules, which affects the pressure term, and (b) the volume occupied by the molecules themselves, which affects the volume term. P + an 2 (V nb ) = nRT V2 P + a (V b ) = RT m V2 m for n moles, and for one mole. The simplest two parameter gas equation in existence. The constants a and b have been experimentally determined for a large number of gases. Provides a natural explanation for critical phenomena. Rearranges to give a closed form expression for pressure: P = RT a2 , Vm b Vm but yields a cubic equation for volume: PV 3 (nbP + nRT)V 2 + aV ab = 0. m m A cubic equation has three roots, which explains the oscillatory behavior of the P-V curve predicted by <a href="/keyword/van-der-waals-equation/" >van der waals equation</a> in the critical region. (See Fig. 1.21). Analysis of the behavior of the <a href="/keyword/van-der-waals-equation/" >van der waals equation</a> in the critical region: 2 P = 0 and P = 0 at V = Vc. V 2 V These two equations and the equation for pressure above can be used to solve for the van der Waals constants a and b and yields an expression for R in terms of the critical variables Pc, Vc and Tc: 8P c V c 1 a = 3P c V 2, b = 3 V c , and R = 3T . c c (1.109) Using these definitions in the <a href="/keyw...