Heat and heat transfer

Thermometers

All thermometers have some property that changes with temperature:

volume of mercurypressure of gas (e.g. pushing against spring)voltage drop across resistorlinear expansion...

Question

Consider a mercury thermometer:

a) Only the mercury expands as it gets hotter

b) Mercury and glass expand equally as it gets hotter

c) The mercury expands much more per degree than glass

Question

A mercury thermometer lying outside in direct sun light measures

a) the air temperature

b) the temperature of the surface of the Sun

c) something else (what?)

Celsius and Fahrenheit

Celsius: 0 °C: (nearly) freezing point of water at standard pressure; 100 °C: boiling point

Fahrenheit: 0 °F is freezing point of a saturated salt water solution, 100 °F is body temperature (he must have been excited…)

0 °C = 32 °F 100 °C = 212 °F

F 32C59

F TT

Questions

A temperature of 100 °F is equal to a temperature of

a) 38 °C b) 56 °C c) 88 °C

A temperature change of 100 °F is equal to a temperature change of

a) 38 °C b) 56 °C c) 88 °C

The Kelvin scale

0 K is absolute zero, 273.16 K is the triple point of water

temperature difference as Celsius

thermometer calibration: 0 K not attainable0 °C redefined as 273.15 K exactlyboiling point of water with constant-volume

thermometer = 99.975 °C

Zeroth Law of Thermodynamics

Temperature measures how hot an object is

Bring hot object in contact with cold object. Temperatures become equal and stay equal

Zeroth law of thermodynamics:

If C is in thermal equilibrium with A and B, then A and B are in thermal equilibrium with each other

Thermal expansion

Small temperature range: expansion linear with temperature increase

Example

An aluminium bar is 0.5 m long at 10 °C. It is heated to 50 °C. What is its length at this temperature? = 2.4 10-5 K-1.

Answer:

Tl

Tll

lll

Tll

10

00

0

0

m 50048.0

00096.15.0

40104.215.0

:5

l

Substitute

Area expansion

All dimensions grow!

From L=L0(1+T):

A = L2 = L02 (1+2T+ 2T2) A0(1+2T)

Aluminium square, T =40 °C : 2T=0.00192, 2T2=0.00000092

Similar for three dimensions

Question

Copper has a coefficient of linear expansion of 1.710-5 K-1. Calculate:

a) in °C-1 and °F-1;

b) the coefficient of volume expansion of copper

A cube of copper has a volume of 6 cm3 at 20 °C. What is its volume at 100 °C?

Bimetallic strips

Bond 2 metals with different

Used as circuit breakerCoiled: thermometer/thermostat

Stress and strain

stress: force per unit area causing a stretch, squeeze or twist

strain: measures resulting deformationHooke’s Law: stress/strain=elastic modulus;

valid over limited rangeYoung’s modulus for tension:

ll

AF

llAF

Y

0

0//

strain tensilestress tensile

Thermal stress

A bar of some material is jammed in between two bodies and is heated

Bar would like to expand by l=l0T

Force needed to oppose this:

Substitute: thermal stress

YAl

lF

0

TYAF

Specific heat I

If we add some heat Q the temperature of an object goes up by T.

Heat needed to raise temperature by T depends on number of molecules in object: Q N

mass is proportional to N , so Q m

Specific heat II

Specific molar heat is proportionality constant when looking at the number of molecules: Q = N C T

Specific heat is proportionality constant when looking at the mass: Q = m c T

Example

The specific heat of the human body is about is 3500 J kg-1 K-1. How much energy is liberated when you have a fever of 39 C?

m = 80 kg; T = 2 C;

Q = 80 3500 2 = 560,000 J !!!

Question

Some people claim that “it is better to get burnt with oil than with water”. The fact that cooking oil is normally used at 180 C while water boils at 100 C suggests that

a) Those people haven’t got a clue

b) Water has a much higher specific heat

c) Water is more aggressive than oil

d) The skin repels the oil

Heat transfer

Conduction: molecular agitation; no motion as a whole

Convection: mass motion of a fluid

Radiation: emission of EM waves, no medium needed

Conduction

Hotter end: molecules jiggle more vigorously & collide with slower ones: net energy transfer

Metals: free electrons for fast energy transferHeat current for constant temperature gradient:

dQ = heat transferred within dt; k = thermal conductivity, L = length/thickness of barrier

LTT

kAtQ

H CH

dd

Conduction II

Generalise for non-uniform temperature gradient:

Ignore minus sign in Young & Freedman

xT

kAtQ

Hdd

dd

Convection

hot air/water expands;becomes less dense;and rises

no simple formula describes convection accurately

Newtonian cooling

Energy transfer model: conduction through thin layer of motionless fluid

Boundary layer has (varying) thickness b, same temperature Tobject

h is heat transfer coefficient

objectfluidobjectfluid

fluiddd

TThAb

TTAk

tQ

H

Thunderstorm formation

Air near ground gets hot and moist

Less dense so rises (Archimedes) and cools

Water vapour condenses/freezes

Rain/hail

Radiation

Emitted power: Pem = e A T4

e: emissivity (0 < e < 1; e = 1 for blackbody) : Stefan-Boltzmann constant = 5.6710-8 W cm-2 K-4

A: radiating area T: absolute temperature

Absorbed power: Pabs = e A Ts4

Ts: absolute temperature of surroundings

PS225 – Thermal Physics topicsThe atomic hypothesisHeat and heat transferKinetic theoryThe Boltzmann factorThe First Law of ThermodynamicsSpecific HeatEntropyHeat enginesPhase transitions