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Chapter 12

Chapter 12. Temperature and Matter. Thermal Physics. Thermal physics is the study of Temperature Heat How these affect matter. Thermal Physics, cont. Concerned with the concepts of energy transfers between a system and its environment and the resulting temperature variations

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Chapter 12

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  1. Chapter 12 Temperature and Matter

  2. Thermal Physics • Thermal physics is the study of • Temperature • Heat • How these affect matter

  3. Thermal Physics, cont • Concerned with the concepts of energy transfers between a system and its environment and the resulting temperature variations • Historically, the development of thermodynamics paralleled the development of atomic theory • Concerns itself with the physical and chemical transformations of matter in all of its forms: solid, liquid, and gas

  4. Zeroth Law of Thermodynamics • If objects A and B are separately in thermal equilibrium with a third object, C, then A and B are in thermal equilibrium with each other. • Allows a definition of temperature

  5. Temperature from the Zeroth Law • Two objects in thermal equilibrium with each other are at the same temperature • Temperature is the property that determines whether or not an object is in thermal equilibrium with other objects

  6. Thermometers • Used to measure the temperature of an object or a system • Make use of physical properties that change with temperature • Many physical properties can be used • volume of a liquid • length of a solid • pressure of a gas held at constant volume • volume of a gas held at constant pressure • electric resistance of a conductor • color of a very hot object

  7. Thermometers, cont • A mercury thermometer is an example of a common thermometer • The level of the mercury rises due to thermal expansion • Temperature can be defined by the height of the mercury column

  8. Temperature Scales • Thermometers can be calibrated by placing them in thermal contact with an environment that remains at constant temperature • Environment could be mixture of ice and water in thermal equilibrium • Also commonly used is water and steam in thermal equilibrium

  9. Celsius Scale • Temperature of an ice-water mixture is defined as 0º C • This is the freezing point of water • Temperature of a water-steam mixture is defined as 100º C • This is the boiling point of water • Distance between these points is divided into 100 segments or degrees

  10. Kelvin Scale • When the pressure of a gas goes to zero, its temperature is –273.15º C • This temperature is called absolute zero • This is the zero point of the Kelvin scale • –273.15º C = 0 K • To convert: TC = TK – 273.15 • The size of the degree in the Kelvin scale is the same as the size of a Celsius degree

  11. Some KelvinTemperatures • Some representative Kelvin temperatures • Note, this scale is logarithmic • Absolute zero has never been reached

  12. Fahrenheit Scales • Most common scale used in the US • Temperature of the freezing point is 32º • Temperature of the boiling point is 212º • 180 divisions between the points

  13. Comparing Temperature Scales

  14. Converting Among Temperature Scales

  15. Gas Thermometer • Temperature readings are nearly independent of the gas • Pressure varies with temperature when maintaining a constant volume

  16. Pressure-Temperature Graph • All gases extrapolate to the same temperature at zero pressure • This temperature is absolute zero

  17. Moles • It’s convenient to express the amount of matter in terms of the number of moles, n • One mole is the amount of the substance that contains as many particles as there are atoms in 12 g of carbon-12

  18. Avogadro’s Number • The number of particles in a mole is called Avogadro’s Number • NA=6.02 x 1023 particles / mole • Defined so that 12 g of carbon contains NA atoms • The mass of an individual atom can be calculated:

  19. Avogadro’s Number and Masses • The mass in grams of one Avogadro's number of an element is numerically the same as the mass of one atom of the element, expressed in atomic mass units, u • Carbon has a mass of 12 u • 12 g of carbon consists of NA atoms of carbon • Holds for molecules, also

  20. Equation of State • Pressure(P), volume(V), temperature(T), and amount of substance(m) are called state variables • State variables are connected • Relationship between state variables is the equation of state

  21. Ideal Gas • A gas does not have a fixed volume or pressure • In a container, the gas expands to fill the container • Most gases at room temperature and pressure behave approximately as an ideal gas

  22. Characteristics of an Ideal Gas • Collection of atoms or molecules that move randomly • Exert no long-range force on one another • Each particle is individually point-like • Occupying a negligible volume

  23. Road to Ideal Gas Law • V is proportional to the number of moles (m/M) (keep P and T constant) • If T is constant, PV=constant (Boyle’s law) • If P is constant, VT (Gay-Lussac’s law)

  24. Ideal Gas Law • PV = (m/M) R T • R is the Universal Gas Constant • R = 8.31 J / mole.K • R = 0.0821 L. atm / mole.K • Is the equation of state for an ideal gas • m is mass of gas • M is molar mass

  25. Ideal Gas Law, cont • Good approximation for real gas at low pressure, quite good at moderate pressure • For a given amount of gas

  26. Ideal Gas Law, more • Standard pressure and temperature (P=1 atm, T=0 °C=273 °K)

  27. Ideal Gas Law, more • Partial pressure concept– total pressure is the sum of partial pressure of the components • Air: O2, N2, C O2, Water vapor, etc.

  28. Example A tank of volume 590 liters contains oxygen at 20 °C and at 5 atm. Calculate the mass of oxygen in the tank. (M=32 kg/kmole for oxygen or 32g/mole)

  29. Example An ideal gas has volume 1 liter at 1 atm and –20 °C. How many atm must it be subjected to when compressed to 0.5 liter at a temperature of 40 °C?

  30. Example The cork of a popgun is inserted so tightly that a pressure of 3 atm is required to dislodge it. Air is admitted through a hole at A, which is 24 cm from the cork at B. How far from A is the piston when the cork pops out, assuming no temperature change?

  31. Kinetic Theory of Gases – Assumptions • The number of molecules in the gas is large and the average separation between them is large compared to their dimensions • The molecules obey Newton’s laws of motion, but as a whole they move randomly

  32. Kinetic Theory of Gases – Assumptions, cont. • The molecules interact only by short-range forces during elastic collisions • The molecules make elastic collisions with the walls • The gas under consideration is a pure substance, all the molecules are identical

  33. Pressure of an Ideal Gas • The pressure is proportional to the number of molecules per unit volume and to the average translational kinetic energy of a molecule

  34. Pressure, cont • The pressure is proportional to the number of molecules per unit volume and to the average translational kinetic energy of the molecule • Pressure can be increased by • Increasing the number of molecules per unit volume in the container • Increasing the average translational kinetic energy of the molecules • Increasing the temperature of the gas

  35. Molecular Interpretation of Temperature • Temperature is proportional to the average kinetic energy of the molecules • The total kinetic energy is proportional to the absolute temperature

  36. Internal Energy • In a monatomic gas, the KE is the only type of energy the molecules can have • U is the internal energy of the gas • In a polyatomic gas, additional possibilities for contributions to the internal energy are rotational and vibrational energy in the molecules

  37. Speed of the Molecules • Expressed as the root-mean-square (rms) speed • At a given temperature, lighter molecules move faster, on average, than heavier ones • Lighter molecules can more easily reach escape speed from the earth

  38. Some rms Speeds

  39. Maxwell Distribution • A system of gas at a given temperature will exhibit a variety of speeds • Three speeds are of interest: • Most probable • Average • rms

  40. Maxwell Distribution, cont • For every gas, vmp < vav < vrms • As the temperature rises, these three speeds shift to the right • The total area under the curve on the graph equals the total number of molecules

  41. Thermal Expansion • The thermal expansion of an object is a consequence of the change in the average separation between its constituent atoms or molecules • At ordinary temperatures, molecules vibrate with a small amplitude • As temperature increases, the amplitude increases • This causes the overall object as a whole to expand

  42. Linear Expansion • For small changes in temperature • , the coefficient of linear expansion, depends on the material Al: 2.4x10^(-5)/C Cu: 1.7x10^(-5)/C Steel: 1.2x10^(-5)/C Glass: 0.4x10^(-5)/C

  43. Applications of Thermal Expansion – Bimetallic Strip • Thermostats • Use a bimetallic strip • Two metals expand differently • Since they have different coefficients of expansion

  44. Area Expansion • Two dimensions expand according to • g is the coefficient of area expansion

  45. Volume Expansion • Three dimensions expand • For some liquids, the coefficient of volume expansion is given here Mercury: 18x10^(-5)/C Ethanol:: 75x10^(-5)/C

  46. More Applications of Thermal Expansion • Pyrex Glass • Thermal expansion are smaller than for ordinary glass • Less thermal stress, used for cooking • Sea levels • Warming the oceans will increase the volume of the oceans

  47. Example A glass flask 200 cm^3 filled with Hg at 20 C. How much mercury will overflow when temperature reaches 100 C? (ignore the expansion of flask)

  48. Unusual Behavior of Water • As the temperature of water increases from 0ºC to 4 ºC, it contracts and its density increases • Above 4 ºC, water exhibits the expected expansion with increasing temperature • Maximum density of water is 1000 kg/m3 at 4 ºC

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