1. Purdue University, Physics 220
Lecture 25
Heat Transfer
Lecture 25
Purdue University, Physics 220

2. Purdue University, Physics 220
Heat transfer
Conduction
Convection
Electro-magnetic radiation
Lecture 25
Purdue University, Physics 220

3. Heat Transfer: Conduction
Hot molecules have more KE than cold molecules
High-speed molecules on left collide with low-speed molecules on right
energy transferred to lower-speed molecules
heat transfers from hot to cold
vibrations
Lecture 25
Purdue University, Physics 220

4. Heat Transfer: Conduction
I = rate of heat transfer = Q/t [J/s]
I = k A (TH-TC)/d
Q/t = k A T/x
k = thermal conductivity
Units: J/s*m*C
good conductors…high k e.g., metal
good insulators … low ke.g., plastic
R = d/(Ak) = thermal resistance
d = Dx TH
Hot TC
Cold
Area A
Lecture 25
Purdue University, Physics 220

5. Purdue University, Physics 220
Conduction
Which of the following is an example of conductive heat transfer?
A) You stir some hot soup with a silver spoon and notice that the spoon warms up.
B) You stand watching a bonfire, but can’t get too close because of the heat.
C) Its hard for central air-conditioning in an old house to cool the attic.
Lecture 25
Purdue University, Physics 220

6. Conduction with 2 Layers
Find I=Q/t in J/s
Key Point: Continuity (just like fluid flow)
I1 = I2
k1A(T0-TC)/Dx1 = k2A(TH-T0)/Dx2
solve for T0 = temp. at junction
then solve for I1 or I2
TH-T0 = I R1 and T0-TC = I R2
T = (TH-T0) + (T0-TC) = I (R1 + R2)
Inside: TH = 25C
Outside: TC = 0C I1 I2 T0
Do transparency w/ problem.
Dx1 = 0.02 m A1 = 35 m2 k1 = J/s*m*C
Dx2 = m A2 = 35 m2 k2 = J/s*m*C
answer: T0=2.27 C I=318 Watts
Lecture 25
Purdue University, Physics 220

7. Purdue University, Physics 220
iClicker
Touch the metal base of a chair and the top of a wooden desk in an air-conditioned room, which feels colder?
A) Base B) Same C) Desk
Both must be the same temperature (room temperature), but metal feels colder because it conducts heat better/faster.
Lecture 25
Purdue University, Physics 220

8. Heat Transfer: Convection
Air heats at bottom
Thermal expansion…density gets smaller
Lower density air rises
Archimedes: low density floats on high density
Cooler air pushed down
Cycle continues with net
result of circulation of air
I = Q/t = h A T
h = coefficient of convection
Practical aspects
heater ducts on floor
A/C ducts on ceiling
stove heats water from bottom
Lecture 25
Purdue University, Physics 220

9. Purdue University, Physics 220
Convection
Lecture 25
Purdue University, Physics 220

10. Purdue University, Physics 220
Convection
Which of the following is an example of convective heat transfer?
A) You stir some hot soup with a silver spoon and notice that the spoon warms up.
B) You stand watching a bonfire, but can’t get too close because of the heat.
C) Its hard for central air-conditioning in an old house to cool the attic.
Lecture 25
Purdue University, Physics 220

11. Purdue University, Physics 220
Convection
Lecture 25
Purdue University, Physics 220

12. Heat Transfer: Radiation
All things radiate / absorb electromagnetic energy
Why? - Because vibration or/and acceleration of charged particles (electrons, protons, ions) results in electromagnetic radiation and vice versa.
No “medium” required
How amount of emitted / absorbed radiation depends on body temperature?
Lecture 25
Purdue University, Physics 220

13. Heat Transfer: Radiation
Iemit = Q/t = eAT4 Stefan-Boltzmann Law
e = emissivity (between 0 and 1)
perfect “black body” has e=1
(What does it mean “black body”?)
T is the temperature of the object (in Kelvin)
 = Stefan-Boltzmann constant = 5.67 x 10-8 J/s*m2*K4
Iabsorb = eAT04
good emitters (e close to 1) are also good absorbers
Lecture 25
Purdue University, Physics 220

14. Purdue University, Physics 220
Question
One day during the winter, the sun has been shining all day. Toward sunset a light snow begins to fall. It collects without melting on a cement playground, but it melts immediately upon contact on a black asphalt road adjacent to the playground. How do you explain this.
The black asphalt absorbs more heat from the sun.
The black asphalt has an emissivity of 1 and absorbs energy from the surrounding (from the sun) compared to a smaller number for the cement. As a result, it is at a higher temperature than the cement and melts the snow.
Lecture 25
Purdue University, Physics 220

15. Heat Transfer: Radiation
All things radiate and absorb electromagnetic energy
Iemit = eAT4
Iabsorb = eAT04
Inet = Iemit - Iabsorb = eA(T4 - T04)
if T > T0, object cools down
if T < T0, object heats up T
Surroundings at T0
Hot stove
Lecture 25
Purdue University, Physics 220

16. Purdue University, Physics 220
Exercise
The Earth has a surface temperature around 270 K and an emissivity of 0.8, while space has a temperature of around 2 K. What is the net power radiated by the earth into free space?
(Radii of the Earth and the Sun are RE = 6.38×106 m, RS = 7×108 m.)
Inet = Iemit - Iabsorb = eA(T4 - T04)
Lecture 25
Purdue University, Physics 220

17. Purdue University, Physics 220
Radiation
Which of the following is an example of radiative heat transfer?
A) You stir some hot soup with a silver spoon and notice that the spoon warms up.
B) You stand watching a bonfire, but cant get too close because of the heat.
C) Its hard for central air-conditioning in an old house to cool the attic.
Lecture 25
Purdue University, Physics 220

18. Purdue University, Physics 220
iClicker
If you place your hand underneath, but not touching, a kettle of hot water (about 80C), you mainly feel the presence of heat from:
A) conduction
B) convection
C) radiation
Lecture 25
Purdue University, Physics 220

19. Purdue University, Physics 220
Radiation Spectrum
How frequency of radiation depends on T?
Infrared: 100 m m
Visible Light: 0.7m-0.4m
Ultraviolet: < 0.4 m
(stars which are hotter than sun)
Wien’s Law: maxT = × 10-3 mK
Lecture 25
Purdue University, Physics 220

20. Purdue University, Physics 220
Night vision goggles
Lecture 25
Purdue University, Physics 220

21. Purdue University, Physics 220
Temperature of the Sun
The Sun appear yellowish, i.e., = 0.5 m. What is the temperature at the surface of the Sun?
m T = x 10-3 m K
T = x 10-3 / 0.5 x 10-6
= 6000 K
Lecture 25
Purdue University, Physics 220

22. Purdue University, Physics 220
Greenhouse Effect
Lecture 25
Purdue University, Physics 220