1. Heat and heat transfer

2. Thermometers zAll thermometers have some property that changes with temperature: zvolume of mercury zpressure of gas (e.g. pushing against spring) zvoltage drop across resistor zlinear expansion z...

3. Question zConsider 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

4. Question zA 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?)

5. Celsius and Fahrenheit zCelsius: 0 °C: (nearly) freezing point of water at standard pressure; 100 °C: boiling point zFahrenheit: 0 °F is freezing point of a saturated salt water solution, 100 °F is body temperature (he must have been excited…) z0 °C = 32 °F 100 °C = 212 °F

6. Questions zA temperature of 100 °F is equal to a temperature of a) 38 °Cb) 56 °Cc) 88 °C zA temperature change of 100 °F is equal to a temperature change of a) 38 °Cb) 56 °Cc) 88 °C

7. The Kelvin scale z0 K is absolute zero, 273.16 K is the triple point of water ztemperature difference as Celsius zthermometer calibration: 0 K not attainable z0 °C redefined as 273.15 K exactly zboiling point of water with constant-volume thermometer = 99.975 °C

8. Zeroth Law of Thermodynamics zTemperature measures how hot an object is zBring hot object in contact with cold object. Temperatures become equal and stay equal zZeroth law of thermodynamics: If C is in thermal equilibrium with A and B, then A and B are in thermal equilibrium with each other

9. Thermal expansion zSmall temperature range: expansion linear with temperature increase

10. 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. zAnswer:

11. Area expansion zAll dimensions grow!  From L=L 0 (1+  T): A = L 2 = L 0 2 (1+2  T+  2  T 2 )  A 0 (1+2  T)  Aluminium square,  T =40 °C : 2  T=0.00192,  2  T 2 =0.00000092 zSimilar for three dimensions

12. Question zCopper has a coefficient of linear expansion of 1.7  10 -5 K -1. Calculate: a)  in °C -1 and °F -1 ; b) the coefficient of volume expansion of copper zA cube of copper has a volume of 6 cm 3 at 20 °C. What is its volume at 100 °C?

13. Bimetallic strips  Bond 2 metals with different  zUsed as circuit breaker zCoiled: thermometer/thermostat

14. Stress and strain zstress: force per unit area causing a stretch, squeeze or twist zstrain: measures resulting deformation zHooke’s Law: stress/strain=elastic modulus; valid over limited range zYoung’s modulus for tension:

15. Thermal stress zA bar of some material is jammed in between two bodies and is heated zBar would like to expand by  l=l 0  T zForce needed to oppose this: zSubstitute: thermal stress

16. Specific heat I zIf we add some heat Q the temperature of an object goes up by  T. zHeat needed to raise temperature by  T depends on number of molecules in object: Q  N zmass is proportional to N, so Q  m

17. Specific heat II zSpecific molar heat is proportionality constant when looking at the number of molecules: Q = N C  T zSpecific heat is proportionality constant when looking at the mass: Q = m c  T

18. Example zThe 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? zm = 80 kg;  T = 2  C; zQ = 80  3500  2 = 560,000 J !!!

19. Question zSome 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

20. Heat transfer zConduction: ymolecular agitation; no motion as a whole zConvection: ymass motion of a fluid zRadiation: yemission of EM waves, no medium needed

21. Conduction zHotter end: molecules jiggle more vigorously & collide with slower ones: net energy transfer zMetals: free electrons for fast energy transfer zHeat current for constant temperature gradient: zdQ = heat transferred within dt; k = thermal conductivity, L = length/thickness of barrier

22. Conduction II zGeneralise for non-uniform temperature gradient: zIgnore minus sign in Young & Freedman

23. Convection zhot air/water expands; zbecomes less dense; zand rises zno simple formula describes convection accurately

24. Newtonian cooling zEnergy transfer model: conduction through thin layer of motionless fluid zBoundary layer has (varying) thickness b, same temperature T object zh is heat transfer coefficient

25. Thunderstorm formation zAir near ground gets hot and moist zLess dense so rises (Archimedes) and cools zWater vapour condenses/freezes zRain/hail

26. Radiation  Emitted power: P em = e  A T 4 ye: emissivity (0 < e < 1; e = 1 for blackbody)   : Stefan-Boltzmann constant = 5.67  10 -8 W cm -2 K - 4 yA: radiating area yT: absolute temperature  Absorbed power: P abs = e  A T s 4 yT s : absolute temperature of surroundings

27. PS225 – Thermal Physics topics zThe atomic hypothesisThe atomic hypothesis zHeat and heat transferHeat and heat transfer zKinetic theoryKinetic theory zThe Boltzmann factorThe Boltzmann factor zThe First Law of ThermodynamicsThe First Law of Thermodynamics zSpecific HeatSpecific Heat zEntropyEntropy zHeat enginesHeat engines zPhase transitionsPhase transitions