Conceptual Physics

Notes on Chapter 15-18

Temperature, Heat, Heat Transfer, change of phase, and

thermodynamics

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

•

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.

http://www.solarcooking.org/plans

/ American Solar Challenge

http://americansolarchallenge.org/events/asc2010

/

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.

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.

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).

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).

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.

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.

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

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

Temperature, Heat, Heat TransferNewton’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).

Temperature, Heat, Heat Transfer

Global Warming & the Greenhouse Effect

• Earth’s atmosphere is transparent to solar energy. This traps the energy…the greenhouse effect.

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.

Chapter 16: Temperature and HeatTemperature 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.

Temperature ScalesCelsius – 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

Thermal ExpansionMost substances expand when heated. They expand in

all dimensionsConceptual 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?

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.

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)

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.

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 lengthR = radius of curvature of heated metal As = Rq = heated length of metal AR+dr = radius of curvature of heated metal Bs+ds = (R+dr)q = length of heated metal B ds = q dr = s0(1+aBDT) - s0(1+aADT)ds = s0 ( aB -– aA )DTds = differential thermal expansion of metals A& B.

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/

http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch4/gaslaws3.html

http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch4/deviation5.html

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HeatHeat 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/litreGasoline has only slightly greater energy density

Mechanical energy can be converted into heat. Examples?

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.

Specific HeatIf you add heat to a substance its temperature will

increase. But how much? That depends on the specific heat of the substance.

Q = mcDTQ = heat addedm= massc = specific heatDT = change in temperatureWater 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).

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

Specific Heat, values

• Table 16-2

Substance Specific Heat [J / (kg K)]

Specific Heat [cal/(kg K)]

Water 4186 1000

Ice 2090 500

Air 1004 240

Gold 129 31

Walker Problem 29, pg 5301.0-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?

ConductionThere are three ways in which heat can be transferred from one object to another:•Conduction – when two objects are in physical contact.

tL

TkAQ

k = thermal conductivityQ = heat transferredA = cross sectional area t = duration of heat transferL = 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?

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.

Substance Thermal Conductivity: kW / (m K)

Gold 291

Glass 0.84

Water 0.60

Wood 0.10

Air 0.023

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.

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 - TS

4]• 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.

Linear Dimension & AreaA disk has radius r. Which is true:1. The circumference of the disk is 2pr and

the area is pr2

2. The circumference of the disk is pr2 and the area is 2pr

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?

1. 0.999

2. 1.000001

3. 1.001

4. 1.0020011.002

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?

1. 0.999

2. 1.000001

3. 1.001

4. 1.0020011.002

Heat Engines, Heat Pumps, and Refrigerators

Getting something useful from heat

40Spring 2009

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”

41Spring 2009

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

42Spring 2009

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

43Spring 2009

Power Plant Arrangement

Heat flows from Th to Tc, turning turbine along the way

44Spring 2009

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

– Qh is 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– Sh is the change in entropy of the hot body

– Sc is 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

45Spring 2009

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

46Spring 2009

The Laws of Thermodynamics

1. Energy is conserved2. Total system entropy can never decrease3. 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

47Spring 2009

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 = cpmT, where cp is the heat capacity

• We need to also point out that a change in heat energy accompanies a change in entropy:

Q = TS(T expressed in K)

• Adding heat increases entropy– more energy goes into random motionsmore randomness (entropy)

48Spring 2009

How much work can be extracted from heat?

Th

Qh

Qc

W = Qh – Qc

Tc

Hot source of energy

Cold sink of energy

heat energy delivered from source

heat energy delivered to sink

externally delivered work:

efficiency = =W work doneQh heat supplied

conservation of energy

Q

49Spring 2009

Let’s crank up the efficiency

Th

Qh

Qc

W = Qh – Qc

Tc

efficiency = =W work doneQh heat supplied

Let’s extract a lot ofwork, and deliver very little heat to the sink

In fact, let’s demand 100%efficiency by sending no heatto the sink: all convertedto useful work

50Spring 2009

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 = TS– The gain in entropy in the sink must at least balance the

loss of entropy in the sourceStot = Sh + Sc = –Qh/Th + Qc/Tc ≥ 0

Qc ≥ (Tc/Th)Qh sets a minimum on Qc

51Spring 2009

What does this entropy limit mean?

• W = Qh – Qc, so W can only be as big as the minimum Qc will allowWmax = Qh – Qc,min = Qh – Qh(Tc/Th) = Qh(1 – Tc/Th)

• So the maximum efficiency is:maximum efficiency = Wmax/Qh = (1 – Tc/Th) = (Th – Tc)/Th

this and similar formulas must have the temperature in Kelvin

• So perfect efficiency is only possible if Tc is zero (in ºK)– In general, this is not true

• As Tc Th, the efficiency drops to zero: no work can be extracted

52Spring 2009

Examples of Maximum Efficiency

• A coal fire burning at 825 K delivers heat energy to a reservoir at 300 K– max efficiency is (825 – 300)/825 = 525/825 = 64%– this power station can not possibly achieve a higher

efficiency based on these temperatures• A car engine running at 400 K delivers heat

energy to the ambient 290 K air– max efficiency is (400 – 290)/400 = 110/400 = 27.5%– not too far from reality

Q

53Spring 2009

Example efficiencies of power plants

Power plants these days (almost all of which are heat-engines)typically get no better than 33% overall efficiency

54Spring 2009

What to do with the waste heat (Qc)?• One option: use it for space-heating locally

55Spring 2009

Overall efficiency greatly enhanced by cogeneration

56Spring 2009

Heat Pumps

Heat Pumps provide a means to very efficiently move heataround, and work both in the winter and the summer

57Spring 2009

Heat Pump Diagram

58Spring 2009

Heat Pumps and Refrigerators: Thermodynamics

Th

Qh

Qc

W = Qh – Qc

Tc

Hot entity(indoor air)

Cold entity(outside air or refrigerator)

heat energy delivered

heat energy extracted

delivered work:

conservation of energy

Just a heat engine runbackwards…

efficiency = =W work doneQh heat delivered

(heat pump)

efficiency = =W work doneQc heat extracted

(refrigerator)

59Spring 2009

Heat Pump/Refrigerator Efficiencies

• Can work through same sort of logic as before to see that:– heat pump efficiency is: Th/(Th – Tc) = Th/T in ºK

– refrigerator efficiency is: Tc/(Th – Tc) = Tc/T in ºK

• Note that heat pumps and refrigerators are most efficient for small temperature differences– hard on heat pumps in very cold climates– hard on refrigerators in hot settings

60Spring 2009

Example Efficiencies

• A heat pump maintaining 20 ºC when it is –5 ºC outside has a maximum possible efficiency of:

293/25 = 11.72– note that this means you can get almost 12 times the heat

energy than you are supplying in the form of work!– this factor is called the C.O.P. (coefficient of performance)

• A freezer maintaining –5 ºC in a 20 ºC room has a maximum possible efficiency of:

268/25 = 10.72– called EER (energy efficiency ratio)

61Spring 2009

Example Labels (U.S. & Canada)

62Spring 2009

Announcements and Assignments

• Chapter 3 goes with this lecture• HW #3 due Thursday 4/23:– primarily Chapter 2-related problems: (show work

or justify answers!); plus Additional problems (on website)

• Remember that Quizzes happen every week– available from Thurs. 1:50 PM until Friday 7:00 PM– three attempts (numbers change)• the better to learn you with