Thermodynamics. Atoms are in constant motion, which increases with temperature.

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1 Thermodynamics SOME DEFINITIONS: THERMO related to heat DYNAMICS the study of motion SYSTEM an object or set of objects ENVIRONMENT the rest of the universe MICROSCOPIC at an atomic or molecular level MACROSCOPIC at a level detectable by our senses THERMODYNAMICS is the study of the relationship between heat and motion. is a macroscopic description of the properties of a system using state variables (e.g. volume, temperature, pressure) Atoms are in constant motion, which increases with temperature.

2 The Phases of Matter Solid Liquid Gas or Vapor Plasma Increasing Temperature Solids and liquids composed of atoms joined together at distances of about m by attractive electrical forces. In gases, vapors and plasmas, the atoms, molecules or ions are in random motion.

3 Temperature Temperature is a measure of how hot or cold an object is. is measured by a thermometer. Thermometers are based on physical properties of objects that change with temperature, for example: volume of a liquid length of a solid pressure of a gas electrical resistance of a solid electrical potential difference between two solids.

4 Common Temperature Scales Fahrenheit: Based on the ability of farm animals to survive for extended periods without attention. (0 F is the coldest and 100 F is the hottest). Celsius or Centigrade: Based on the physical properties of water on the earth s surface at sea level (0 C is the freezing point and 100 C is the boiling point). T( C) = (5/9)[T( F) 32] T ( F) = (9/5)T( C) + 32

5 Zero th Law of Thermodynamics Our experience tells us that objects placed in contact will eventually reach the same temperature. We say that they are then in thermal equilibrium. This is the basis for The Zero th Law of Thermodynamics: If two objects A and B are in thermal equilibrium with a third object C, then A and B are in thermal equilibrium with each other. Objects or systems in thermal equilibrium have the same temperature. This is the physical basis for the definition of temperature.

6 Questions Is it possible for two objects to be in thermal equilibrium if they are not touching each other? Can objects that have different temperatures be in thermal equilibrium with each other?

7 Thermal Expansion Most materials expand when heated: The average distance between atoms increases as the temperature is raised. The increase is proportional to the change in temperature (over a small range). Consider an object of length L i at temperature T i If the object is heated or cooled to temperature T f L f L i = α L i (T f T i ) or L = α L i T α = coefficient of linear expansion [ºC -1 ] (α is a property of the material)

8 Thermal Expansion of Solids and Liquids Material Glass Concrete Copper Lead Mercury Gasoline α (ºC -1 ) 9 x x x x x x 10-4 For the same temperature change, the thermal expansion of liquids is much greater than that of solids (> 10 times). Area Expansion: A = 2α A i T Volume Expansion V = 3α V i T

9 Example: Thermal Expansion Problem A concrete highway is built of slabs 12 m long (20 ºC). How wide should the expansion cracks between the slabs be (at 20 ºC) to prevent buckling if the range of temperature is 30 ºC to +50 ºC?

10 Liquid water has an unusual property. g/(cm**3) Density of Water Temperature in Celsius Water contracts when heated from 0ºC to 4ºC, then expands when heated from 4 ºC to 100 ºC. Just above the freezing point, the coldest (and least dense) water rises to the surface, and lakes freeze from the surface downward. This unusual property permits aquatic life on earth to survive winter!

11 Thermal Stress T E A F T L L A F E T L L L A F E L = = = = α α α Heat can stress materials if no allowance is made for thermal expansion: E = Young s Modulus Thermal Expansion Thermal Stress

12 Review Questions When a cool mercury or alcohol thermometer is inserted into boiling water, it will initially indicate a lower temperature before the reading starts to increase. Explain. Will a grandfather clock that has been calibrated at normal room temperature run fast, slow or the same on a very hot day?

13 Absolute (Kelvin) Temperature Scale The volume occupied by any gas at constant pressure is an increasing linear function of temperature, that always extrapolates to zero at ºC (called absolute zero). T(K) = T(ºC) This is called Charles s Law and is the basis for the absolute or Kelvin (K) temperature scale.

14 Absolute or Kelvin Temperature Scale The absolute or Kelvin scale is the true physical temperature scale. T = ºC = 0 K is the lowest temperature that can be defined for any physical system. Absolute zero of temperature (0 K) is a theoretical limit that can never be reached in a physical system. Experiments on Bose-Einstein Condensation in gases have reached the nano-kelvin (10-9 K) range (1998, 2001 Nobel Prizes in physics)! The degree steps in the Celsius and Kelvin scales are chosen to be the same: T(ºC) = T(K).

15 Molecular Model of an Ideal Gas The number of molecules is large. The average separation between molecules is large compared to their dimensions. The molecules obey Newton s laws of motion and move randomly. The molecules collide elastically with each other and with the container walls. The forces between molecules are negligible except during collisions. All the molecules of the gas are identical.

16 Ideal Gas The relationship between the state variables, pressure P, volume V and temperature T of a system is called its equation of state. An ideal gas is one whose equation of state is simple: PV = nrt n = number of moles (mole = x molecules) R = universal gas constant = 8.31 J/(mole K) Most gases near room temperature and atmospheric pressure behave as ideal gases.

17 Avogradro s Number and Molar Mass N A = x = Avogadro s number 1 mole is the quantity of any substance that contains Avogadro s number of atoms or molecules. The gram-molecular-weight M of a substance is the mass of one mole (molar mass) of that substance: Helium (He) M = 4 g/mole Nitrogen (N 2 ) M = 28 g/mole Oxygen (O 2 ) M = 32 g/mole Methane (CH 4 ) M = 16 g/mole

18 Equation of State of an Ideal Gas For a gas containing N atoms or molecules, the number of moles n = N/N A. The ideal gas law: PV = nrt = (N/N A )RT = N(R/N A )T = Nk B T where k B = R/N A = 1.38 x J/K (Boltzmann s constant) The ideal gas law may be expressed: PV = Nk B T (N = number of atoms or molecules) or PV = nrt (n = number of moles)

19 Applying the Ideal Gas Law For a ideal gas: INITIAL STATE (1) FINAL STATE (2) P 1, V 1, T 1, n 1 P 2, V 2, T 2, n 2 P 1 V 1 = n 1 RT 1 P 2 V 2 = n 2 RT 2 R = P 1 V 1 /(n 1 T 1 ) R = P 2 V 2 /(n 2 T 2 ) P V PV P V PV 1 1 = or if n = n T n T 1 = n 2 T T general case closed container

20 Problem Example Problem If mol of helium gas is at 10.0ºC and a gauge pressure of atm., calculate a) The volume of the helium gas under these conditions. b) The temperature if the gas is compressed to precisely half the volume at a gauge pressure of 1.00 atm.

21 Questions An ideal gas in a sealed bottle at temperature T occupies a volume V, and exerts a pressure P on the walls of the bottle. What will happen to the pressure if the temperature is doubled? Instead of a sealed container, the gas is contained in a test tube with a movable piston on one end. The temperature is then halved. What will happen to a) the pressure? b) the volume?

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