Post on 20-Dec-2015
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