Conceptual Physics

1. Conceptual Physics Notes on Chapter 15-18 Temperature, Heat, Heat Transfer, change of phase, and thermodynamics

2. Temperature • All matter—solid, liquid, and gas—is composed of continuously jiggling atoms or molecules. • Because of this random motion, the atoms and molecules in matter have kinetic energy • When a solid, liquid, or gas gets warmer, its atoms or molecules move faster • The increased movement causes an increase in heat

3. Thermometer • The first “thermal meter” for was invented by Galileo in 1602 • The familiar mercury-in-glass thermometer came into widespread use some seventy years later. • Mercury thermometers are being phased out because of the danger of mercury poisoning • We express the temperature of some quantity of matter by a number that corresponds to its degree of hotness or coldness on some chosen scale. • Nearly all materials expand when their temperature is raised and contract when their temperature is lowered. Most thermometers measure temperature by means of the expansion or contraction of a liquid, usually mercury or colored alcohol, in a glass tube with a scale.

5. http://www.solarcooking.org/plans/ American Solar Challenge http://americansolarchallenge.org/events/asc2010/

6. Temperature, Heat, Heat Transfer • This is going to be a REVIEW of last years chemistry class. • However, we are going to look at this from a PHYSICS perspective.

7. Temperature, Heat, Heat Transfer • All matter is composed of “jiggling” atoms. This matter has kinetic energy (Ch.8). • This kinetic energy causes an effect we call warmth or TEMPERATURE. • Cold objects have Less kinetic energy. • Hot objects have More kinetic energy.

8. Temperature, Heat, Heat Transfer • Most objects expand when it gains energy and contracts when it losses energy. A Thermometer is a good example. • Celsius Scale • Fahrenheit Scale • Kelvin Scale • Celsius Scale – named in honor of astronomer Andres Celsius (1701 – 1744). • Fahrenheit Scale - named in honor of German physicist Gabriel Fahrenheit (1686 – 1736). • Kelvin Scale - named in honor of British physicist Lord Kelvin (1824 – 1907).

9. Temperature, Heat, Heat Transfer • The energy that transfers from one object to another because of a temperature difference between them is called HEAT. • Note: Matter DOES NOT contain heat. • Matter contains ENERGY in the form of heat. • The grand total of all energies inside a substance is called INTERNAL ENERGY. • A substance that does not contain heat, still contains internal energy (atoms vibrating).

10. Temperature, Heat, Heat Transfer Measurement of Heat • The most common unit of heat is the CALORIE. The calorie is defined as the amount of heat required to raise the temperature of 1 gram of water by 1°C. • IMPORTANT: Calorie and calorie are both units of energy. Calorie is the Food version.

11. Temperature, Heat, Heat Transfer Specific Heat Capacity • Different objects have different capacities for storing internal energy. • Aluminum foil cools very rapidly…food in container does not! • We call this Specific heat capacity.

12. Temperature, Heat, Heat Transfer Applications • This leads to increased “jiggle” of atoms which tend to move apart. The result is EXPANSION of the substance. • Bimetallic strip … Thermostat • Bridge Gaps • Jar lids

13. Temperature, Heat, Heat Transfer Conduction, Convection, Radiation • Conduction • The direct transfer or movement of warmth and energy from one molecule to another molecule by collision. • Convection • The organized motion or movement of large groups of molecules based on their relative densities or temperatures. • Radiation • The method by which the sun's energy reaches the earth

14. Temperature, Heat, Heat Transfer Newton’s Law of Cooling • Newton's Law of Cooling states that the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature (i.e. the temperature of its surroundings).

15. Temperature, Heat, Heat Transfer Global Warming & the Greenhouse Effect • Earth’s atmosphere is transparent to solar energy. This traps the energy…the greenhouse effect.

16. Temperature, Heat, Heat Transfer Global Warming & the Greenhouse Effect • This is good in that it helps heat the earth. • HOWEVER…to much heating leads to global warming.

17. Chapter 16: Temperature and Heat Temperature is a fundamental quantity which characterizes the physical state of a substance. In the microscopic statistical theory, we understand temperature as the average energy per degree of freedom of motion of the substance. Heat is an interaction between two objects, particularly the flow of energy from one object to another. When two objects are placed in thermal contact (so that heat is able to flow from one to the other), heat will flow until the temperatures of the two objects are the same. Then the two objects are in thermal equilibrium.

18. Temperature Scales Celsius – water freezes at 0 °C and boils at 100 °C Fahrenheit – water freezes at 32 °F and boils at 212 °F Kelvin - water freezes at 273.15 K and boils at 373.15 K. But how do we determine the equal divisions between these calibration points? Absolute Zero – the lowest possible temperature: 0 K = –273.15 °C TK = TC + 273.15

19. Thermal Expansion Most substances expand when heated. They expand in all dimensions Conceptual Checkpoint 16-3: A washer has a hole in the middle. As the washer is heated does the hole (a) expand, (b) shrink, or (c) stay the same? Hint, what happens to the piece cut out to make the hole?

20. Water is special! Water is an exception to the rule. Between 0 and 4 °C it contracts. Above 4 °C it expands. Water is most dense at 4 °C. Precurser to fact that ice floats! (most solids sink in their own liquid) Thermal Expansion.

21. Thermometers & Thermostats • Use the expansion of Hg to define a temperature scale. • Use the differential expansion of two dissimilar metals to make either a thermometer or a thermostat (temperature activated switch)

22. Thermal Expansion Coefficient • Any linear dimension L of a solid object with expand (or contract) with temperature changes. • If L is the length at temperature T0, then • L(T0 +DT) = L + DL • DL = a L DT • (DL/L) = a DT • a is the coefficient of linear expansion • a itself can be a function of temperature • a(water) < 0 for 0º C < T < 4º C • a(Cu) = 17·10-6 / (º C) • 1degree Celsius change causes a fractional expansion of 17 parts per million.

23. Thermometers & Thermostats • Use the expansion of Hg to define a temperature scale. • Use the differential expansion of two dissimilar metals to make either a thermometer or a thermostat (temperature activated switch) s0 = unheated common length R = radius of curvature of heated metal A s = Rq = heated length of metal A R+dr = radius of curvature of heated metal B s+ds = (R+dr)q = length of heated metal B ds = qdr = s0(1+aBDT) - s0(1+aADT) ds = s0 ( aB-– aA )DT ds = differential thermal expansion of metals A& B.

24. Absolute Zero • Ideal Gas Law (Chapter 17) • Constant Volume Gas-Thermometer. • Keep the reference level fixed = fixed gas volume. • Adjust height as temperature of gas is varied • Pressure of gas = r g h • Pressure curves extrapolate to a common zero pressure at a common temperature • T = -273.15 C = -460F http://jersey.uoregon.edu/vlab/Piston/

25. http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch4/gaslaws3.htmlhttp://chemed.chem.purdue.edu/genchem/topicreview/bp/ch4/gaslaws3.html H2 & N2 at 0deg C CO2 at 40deg C http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch4/deviation5.html

26. Heat Heat Q is the energy transferred between one object and another due to temperature differences. Heat is measured in calories (cal). 1 cal = 4.186 J A Calorie (C) is a kilocalorie. Salad oil: 8.6kC / kg  8.6 kC /litre=36·106 J/litre Gasoline has only slightly greater energy density Mechanical energy can be converted into heat. Examples?

27. Solar Energy & Agriculture • The solar flux is 1 kW/m2. • The atmosphere absorbs about ½, we lose ½ for night time, the growing season is ½ the year, ½ the days are cloudy. • Modern agriculture is about 3% efficient at turning solar energy into plant chemical energy. Assume ¼ of this can be recovered in a seed oil (sunflower, etc), convertible to diesel. • Total yield of 1 hectare: 100m x 100 m • (1000 W/m2) (104 m2) (1/2)4 (0.03) (1/4)  1 Cal/s • Gasoline consumption 1 gallon/person/day • 1 gallon oil/day  34,000 Cal/day = 0.4 Cal/s • We could power all of our vehicles on bio-diesel, • But modern agriculture uses 1 gallon of fossil fuel to make 1 gallon of bio-diesel. • Need a non-fossil fuel dependent agriculture.

28. Specific Heat If you add heat to a substance its temperature will increase. But how much? That depends on the specific heat of the substance. Q = mcDT Q = heat added m= mass c = specific heat DT = change in temperature Water has a very large heat capacity; a lot of energy transfer (heat) is required to change its temperature. This has a major impact on the climate. Water: c = 1.0 cal /(ºC g) = 1.0 Cal /(ºC kg) It takes one calorie to raise the temperature of 1 gm of water by 1 degree Celsius (use this to define 1 calorie).

29. Mechanical Equivalent of Heat • Conservation of energy can be broadened to include thermal energy • Work done on system by non-conservative forces = heat = thermal energy added to system • Rub your hands to warm them (work done by friction). • 1 calorie = 4.18 Joule

30. Specific Heat, values • Table 16-2

31. Walker Problem 29, pg 530 1.0-g lead pellets at 75 °C are to be added to 180 g of water at 22 °C. How many pellets are needed to increase the equilibrium temperature to 25 °C?

32. Conduction • There are three ways in which heat can be transferred from one object to another: • Conduction – when two objects are in physical contact. k = thermal conductivity Q = heat transferred A = cross sectional area t = duration of heat transfer L = length DT = temperature difference between two ends In a hot oven the air and the metal rack are at the same temperature, but which one feels hotter and why?

33. Thermal Conductivities, Table 16-3 • Metals have high thermal conductivity, most electrical insulators also have low thermal conductivity. • Air is a great insulator, except that large air spaces allow heat flow by convection.

34. Convection and Radiation • Convection – when heat is carried by a moving fluid • Heat house with radiator • Gulf stream transports Heat from Caribbean to Europe • Cold air inside window (in winter) sinks, creates convection = cold draft • Radiation – when electromagnetic waves (radiation) carry heat from one object to another. • Example: heat you feel when you are near a fire • Example: Heat from the sun • Formation of frost (ice) at night, • T(air) > 0ºC, but surface temp drops below 0ºC.

35. Black Body Radiation • Any object heated to a temperature T (on an absolute scale) radiates Electromagnetic Energy (light) with total power: P = e s A T4 • 0<e<1 = emissivity = property of material • s = 5.67 ·10 –8 W/(m2 K4) • A = surface area of object • Peak wavelength occurs at l = (5.1·10-3 m ·K ) / T (Chap 30) • Early triumph of quantum theory (M. Planck) to predict Power and wavelength equations, including the values of the constants, with just one free parameter (now called Planck’s constant). • If the surroundings have temperature TS, then the net power radiated is • P = e s A [ T4 - TS4] • Dark, dry, night, TS = 3 K, Black body radiation cools the surface faster than conduction can transport heat from the ground or air. Frost can form even if air temperature > 0C.

36. Linear Dimension & Area A disk has radius r. Which is true: • The circumference of the disk is 2pr and the area is pr2 • The circumference of the disk is pr2 and the area is 2pr

37. Thermal Expansion A metal disk of radius r = 5.00 cm and thickness d=1.00mm is heated such that every linear dimension expands to 1.001 times its original length. • What is the fractional change fC=(2pr’)/(2pr) in the circumference of the disk? • 0.999 • 1.000001 • 1.001 • 1.0020011.002

38. Thermal Expansion A metal disk of radius r = 5.00 cm and thickness d=1.00mm is heated such that every linear dimension expands to 1.001 times its original length. • What is the fractional change fA=(pr’2)/(pr2) in the area of the disk? • 0.999 • 1.000001 • 1.001 • 1.0020011.002

39. Heat Engines, Heat Pumps, and Refrigerators Getting something useful from heat

40. Heat can be useful • Normally heat is the end-product of the flow/transformation of energy • remember examples from lecture #4 (coffee mug, automobile, bouncing ball) • heat regarded as waste: as useless end result • Sometimes heat is what we want, though • hot water, cooking, space heating • Heat can also be coerced into performing “useful” (e.g., mechanical) work • this is called a “heat engine”

41. Heat Engine Concept • Any time a temperature difference exists between two bodies, there is a potential for heat flow • Examples: • heat flows out of a hot pot of soup • heat flows into a cold drink • heat flows from the hot sand into your feet • Rate of heat flow depends on nature of contact and thermal conductivity of materials • If we’re clever, we can channel some of this flow of energy into mechanical work

42. Heat  Work • We can see examples of heat energy producing other types of energy • Air over a hot car roof is lofted, gaining kinetic energy • That same air also gains gravitational potential energy • All of our wind is driven by temperature differences • We already know about radiative heat energy transfer • Our electricity generation thrives on temperature differences: no steam would circulate if everything was at the same temperature

43. Power Plant Arrangement Heat flows from Th to Tc, turning turbine along the way

44. Heat Engine Nomenclature • The symbols we use to describe the heat engine are: • Th is the temperature of the hot object (typ. in Kelvin) • Tc is the temperature of the cold object (typ. in Kelvin) • T = Th–Tc is the temperature difference • Qhis the amount of heat that flows out of the hot body • Qc is the amount of heat flowing into the cold body • W is the amount of “useful” mechanical work • Shis the change in entropy of the hot body • Scis the change in entropy of the cold body • Stot is the total change in entropy (entire system) • E is the entire amount of energy involved in the flow

45. What’s this Entropy business? • Entropy is a measure of disorder (and actually quantifiable on an atom-by-atom basis) • Ice has low entropy, liquid water has more, steam has a lot

46. The Laws of Thermodynamics • Energy is conserved • Total system entropy can never decrease • As the temperature goes to zero, the entropy approaches a constant value—this value is zero for a perfect crystal lattice • The concept of the “total system” is very important: entropy can decrease locally, but it must increase elsewhere by at least as much • no energy flows into or out of the “total system”: if it does, there’s more to the system than you thought Q

47. Quantifying heat energy • We’ve already seen many examples of quantifying heat • 1 Calorie is the heat energy associated with raising 1 kg (1 liter) of water 1 ºC • In general, Q = cpmT, where cp is the heat capacity • We need to also point out that a change in heat energy accompanies a change in entropy: Q = TS (T expressed in K) • Adding heat increases entropy • more energy goes into random motionsmore randomness (entropy)

48. Th Qh W = Qh– Qc Qc W work done efficiency = = Qh heat supplied Tc How much work can be extracted from heat? Hot source of energy heat energy delivered from source externally delivered work: conservation of energy heat energy delivered to sink Cold sink of energy Q

49. Th Qh W = Qh– Qc Qc W work done efficiency = = Qh heat supplied Tc Let’s crank up the efficiency Let’s extract a lot of work, and deliver very little heat to the sink In fact, let’s demand 100% efficiency by sending no heat to the sink: all converted to useful work

50. Not so fast… • The second law of thermodynamics imposes a constraint on this reckless attitude: total entropy must never decrease • The entropy of the source goes down (heat extracted), and the entropy of the sink goes up (heat added): remember that Q = TS • The gain in entropy in the sink must at least balance the loss of entropy in the source Stot = Sh + Sc = –Qh/Th + Qc/Tc≥ 0 Qc ≥ (Tc/Th)Qh sets a minimum on Qc