Molecular Speeds. Real Gasses. Ideal Gas Law. Reasonable. Why the breakdown? P-V Diagram. Using moles. Using molecules

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1 Kinetic Theory of Gases Connect icroscopic properties (kinetic energy and oentu) of olecules to acroscopic state properties of a gas (teperature and pressure). P v v But K v and P kt K v kt Teperature is a easure of the average kinetic energy (internal energy?) of the gas. For constant volue, pressure increases directly proportional to an increase in average kinetic energy (teperature) AD an increase in the nuber of olecules. Molecular Speeds Since 3 3kT K v kt v v Distribution of olecular speeds, The Maxwell-Boltzann distribution v 3 kt f ( v) 4π v e ote 0 πkt f ( v) dv 8kT v vf ( v) dv 0 π 3kT v rs v f ( v) dv 0 v p rs df ( v) 0 dv v p kt Ideal Gas Law Using oles P n nuber of oles R universal gas constant 8.35 J / (ol-k) Using olecules P kt nuber of olecules k Boltzann s constant.38 x 0-3 J / K This is called the Equation of State. Why Ideal? Dilute, olue of Molecules is ~ Zero o Attractions Between Molecules Teperature ust be in Absolute Units, K Real gases do not follow the ideal gas law precisely. However, at low pressure and teperatures not too close to the liquefaction point, the ideal gas law is quite accurate and useful for real gases. Real Gasses Reasonable Pressure not too high ot near liquefaction point Why the breakdown? ear liquefaction Interolecular forces atter P- Diagra Each line is at a constant teperature Solid Real, Dashed Ideal Point c is the critical point, curve C is critical tep.

2 Phase Diagras Triple Point is iportant as a reference standard What happens above the critical point? apor Pressure Since the liquid has a distribution of olecular speeds Soe olecules will escape Evaporation Since the gas has a distribution of olecular speeds Soe olecules will be recaptured Condensation The gas will exert a vapor pressure At equilibriu: saturated vapor pressure (SP) This is teperature dependent. apor Pressure apor pressure explains boiling Liquid teperature SP teperature Boiling occurs Law of partial pressures The total pressure of a ixture of gasses the su of vapor pressure of the constituent gasses P T P + P + Relative Huidity What is the teperature on a day when the partial pressure of water is 530 Pa and the relative huidity is 40.0%? partial pressure of H O RH SP of H O 00% Dew Point: Teperature at which unsaturated air will becoe saturated.

3 Real Gasses - Better Approxiations Ideal Gas First Order Clausius Equation of State (EoS) P nb Second Order an der Waals P nb P a ( / n) Mean Free Path Molecular concentration Assue the other olecules are not oving, then the nuber of olecules in the cylinder is C cyl π (r) vδt Mean Free Path is average distance between collisions d vδt l M C π ( r) vδt 4πr If you account for the oveent of the other olecules l M 4 πr Rando Walk - Diffusion On average, the diffusing substance will ove fro a region of high concentration to a region of low concentration. Why? A student walks across a field that is 60 x 40. Estiate the student s ean free path if there are (a) 0, (b) 00, (c) 300 other students on the field. J C C DA Δx J Rate of Diffusion D Diffusion Constant (gas dependent) A Cross-Sectional Area 3

4 Heat What is heat? What do we ean when we say soething is hot or cold? Is heat the sae as teperature? What do we know about teperature? It is a easure of internal energy. It is a easure of the closeness of theral equilibriu. What happens when two systes that are not in theral equilibriu coe in contact? Energy will be transferred fro the higher teperature syste to the lower energy syste until theral equilibriu is reached that is they have the sae teperature. Heat What is heat? Heat (Q) is the flow or transfer of energy fro one syste to another Often referred to as heat flow or heat transfer Requires that one syste ust be at a higher teperature than the other Heat will only flow fro the syste with the higher teperature to the syste with the lower teperature Heat will only flow fro the syste with the higher average internal energy to the syste with the lower average internal energy Total internal energy does not atter. Heat Units Since heat is the flow of energy fro one syste to another, the standard SI unit is the joule J Traditional unit is the calorie (cal) cal is the heat needed to raise g of water fro 4.5 C to 5.5 C A kilocalorie (kcal) or Calorie (Cal) is 000 cal Used to easure energy content of food Conversion 4.86 J cal, 4.86 x 0 3 J kcal British Theral Unit (Btu) kcal 3.97 Btu Heat Capacity When the teperature of syste changes, there has been heat flow Q Heat capacity connects heat flow to teperature change: Q CΔT Heat capacity C depends on the aterial and also on the quantity of aterial present. Eliinate quantity dependence by introducing specific heat c and olar heat capacity c : Q cδt Q nc ΔT ass n nuber of oles 4

5 Specific Heats and Molar Heat Capacities Measuring Heat Capacities Calorieter Syste is adiabatically isolated fro the environent et Q 0 fro or into the device Heat lost heat gained Conservation of energy An axe head consisting of.8 kg of iron is left outdoors one cold winter s night and is brought indoors when the outside teperature is a brisk 40K. The roo into which it is brought is initially at a nice, cofortable 93K and.0 at of pressure. The volue of the roo, which is well insulated, is Assuing that the axe head coes to theral equilibriu with the air in the roo, by how uch is the teperature of the roo lowered? (Ignore the theral interaction with furniture, walls, and so forth. Use c air 0.7 cal/g-k and 8.8 g/ol for the olecular weight of air.) 5