1. Chapter 12 Temperature and Matter

2. Thermal Physics Thermal physics is the study of Thermal physics is the study of TemperatureTemperature HeatHeat How these affect matterHow 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 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 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 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. 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 Allows a definition of temperature

5. Temperature from the Zeroth Law Two objects in thermal equilibrium with each other are at the same temperature 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 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 Used to measure the temperature of an object or a system Make use of physical properties that change with temperature Make use of physical properties that change with temperature Many physical properties can be used Many physical properties can be used volume of a liquidvolume of a liquid length of a solidlength of a solid pressure of a gas held at constant volumepressure of a gas held at constant volume volume of a gas held at constant pressurevolume of a gas held at constant pressure electric resistance of a conductorelectric resistance of a conductor color of a very hot objectcolor of a very hot object

7. Thermometers, cont A mercury thermometer is an example of a common thermometer A mercury thermometer is an example of a common thermometer The level of the mercury rises due to thermal expansion The level of the mercury rises due to thermal expansion Temperature can be defined by the height of the mercury column 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 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 equilibriumEnvironment could be mixture of ice and water in thermal equilibrium Also commonly used is water and steam in thermal equilibriumAlso commonly used is water and steam in thermal equilibrium

9. Celsius Scale Temperature of an ice-water mixture is defined as 0º C Temperature of an ice-water mixture is defined as 0º C This is the freezing point of waterThis is the freezing point of water Temperature of a water-steam mixture is defined as 100º C Temperature of a water-steam mixture is defined as 100º C This is the boiling point of waterThis is the boiling point of water Distance between these points is divided into 100 segments or degrees 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 When the pressure of a gas goes to zero, its temperature is –273.15º C This temperature is called absolute zero This temperature is called absolute zero This is the zero point of the Kelvin scale This is the zero point of the Kelvin scale –273.15º C = 0 K–273.15º C = 0 K To convert: T C = T K – 273.15 To convert: T C = T K – 273.15 The size of the degree in the Kelvin scale is the same as the size of a Celsius degreeThe size of the degree in the Kelvin scale is the same as the size of a Celsius degree

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

12. Fahrenheit Scales Most common scale used in the US Most common scale used in the US Temperature of the freezing point is 32º Temperature of the freezing point is 32º Temperature of the boiling point is 212º Temperature of the boiling point is 212º 180 divisions between the points 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 Temperature readings are nearly independent of the gas Pressure varies with temperature when maintaining a constant volume Pressure varies with temperature when maintaining a constant volume

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

17. Moles It’s convenient to express the amount of matter in terms of the number of moles, n 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 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 The number of particles in a mole is called Avogadro’s Number N A =6.02 x 10 23 particles / moleN A =6.02 x 10 23 particles / mole Defined so that 12 g of carbon contains N A atomsDefined so that 12 g of carbon contains N A atoms The mass of an individual atom can be calculated: 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 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 Carbon has a mass of 12 u 12 g of carbon consists of N A atoms of carbon12 g of carbon consists of N A atoms of carbon Holds for molecules, also Holds for molecules, also

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

21. Ideal Gas A gas does not have a fixed volume or pressure A gas does not have a fixed volume or pressure In a container, the gas expands to fill the container In a container, the gas expands to fill the container Most gases at room temperature and pressure behave approximately as an ideal gas 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 Collection of atoms or molecules that move randomly Exert no long-range force on one another Exert no long-range force on one another Each particle is individually point-like Each particle is individually point-like Occupying a negligible volumeOccupying a negligible volume

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

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

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

26. Ideal Gas Law, more Standard pressure and temperature (P=1 atm, T=0 °C=273 °K) 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 Partial pressure concept– total pressure is the sum of partial pressure of the components Air: O 2, N 2, C O 2, Water vapor, etc. Air: O 2, N 2, C O 2, 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 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 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 interact only by short- range forces during elastic collisions The molecules make elastic collisions with the walls The molecules make elastic collisions with the walls The gas under consideration is a pure substance, all the molecules are identical 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 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 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 Pressure can be increased by Increasing the number of molecules per unit volume in the containerIncreasing the number of molecules per unit volume in the container Increasing the average translational kinetic energy of the moleculesIncreasing the average translational kinetic energy of the molecules Increasing the temperature of the gas Increasing the temperature of the gas

35. Molecular Interpretation of Temperature Temperature is proportional to the average kinetic energy of the molecules Temperature is proportional to the average kinetic energy of the molecules The total kinetic energy is proportional to the absolute temperature 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 In a monatomic gas, the KE is the only type of energy the molecules can have U is the internal energy of the gas 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 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 Expressed as the root-mean-square (rms) speed At a given temperature, lighter molecules move faster, on average, than heavier ones At a given temperature, lighter molecules move faster, on average, than heavier ones Lighter molecules can more easily reach escape speed from the earthLighter 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 A system of gas at a given temperature will exhibit a variety of speeds Three speeds are of interest: Three speeds are of interest: Most probableMost probable AverageAverage rmsrms

40. Maxwell Distribution, cont For every gas, v mp < v av < v rms For every gas, v mp < v av < v rms As the temperature rises, these three speeds shift to the right 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 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 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 At ordinary temperatures, molecules vibrate with a small amplitude As temperature increases, the amplitude increases As temperature increases, the amplitude increases This causes the overall object as a whole to expandThis causes the overall object as a whole to expand

42. Linear Expansion For small changes in temperature For small changes in temperature, the coefficient of linear expansion, depends on the material, 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 Thermostats Use a bimetallic strip Two metals expand differently Since they have different coefficients of expansion

44. Area Expansion Two dimensions expand according to Two dimensions expand according to  is the coefficient of area expansion

45. Volume Expansion Three dimensions expand Three dimensions expand For some liquids, the coefficient of volume expansion is given hereFor 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 Pyrex Glass Thermal expansion are smaller than for ordinary glassThermal expansion are smaller than for ordinary glass Less thermal stress, used for cookingLess thermal stress, used for cooking Sea levels Sea levels Warming the oceans will increase the volume of the oceansWarming 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 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 Above 4 ºC, water exhibits the expected expansion with increasing temperature Maximum density of water is 1000 kg/m 3 at 4 ºC Maximum density of water is 1000 kg/m 3 at 4 ºC