1. PHYSICS 231 INTRODUCTORY PHYSICS I
Lecture 17

2. Recap - Heat Transfer
Heat: Q = Energy transferred due to microscopic contact
Heat can:
Change temperature
c = specific heat
For water: c= 1.0 cal/(g°C)
Change state of matter
L = Latent heat of fusion or vaporization
For water: LF=79.7 cal/g, LV=540 cal/g

3. Example 11.11
A 50 g ice cube at 0ºC is put into a styrofoam cup containing 300 g of coffee at 90ºC. Assuming no heat is lost to the cup or the air, what is the final temperature of the coffee after the ice melts?
T = 65.8°C

4. Recap - Kinds of Heat Transfer
Conduction
Hot and cold objects in physical contact
Examples: Heating a skillet, losing heat through the walls
Convection
Hot objects move (gas or liquid)
Examples: Hot-water heating for buildings Circulating air Unstable atmospheres
Radiation
Energy transferred by light (UV, IR,…)
Examples: Stars, Incandescent bulbs

5. Conduction Rate of heat transfer Conductivity k is property of
material
R-value also depends
on thickness. It adds for
layered objects (R=R1+R2)

6. Example 11.12
What is the ratio of heat transfer for a single pane of glass (1 cm thick) to that of a double pane of glass (each 0.5 cm thick with 1 mm air between)?
DATA: kglass= 0.84 W/mºC, kair= W/m ºC
P1/P2 = 4.59

7. Convection Due to movement of hot gas or liquid
Hot air rises from radiator causing air currents
Air trapped between glass panes cannot transfer heat by convection, only conduction.

8. Transfer of heat by radiation
All objects emit light if T > 0
Colder objects emit longer wavelengths (red or infra-red)
Hotter objects emit shorter wavelengths (blue or ultraviolet)
Stefan’s Law give power of emitted radiation
Emissivity, 0 < e < 1, usually near 1
s = x10-8 W/(m2ºK4)
is the Stefan-Boltzmann constant
T must be in Kelvin !!!

9. Example 11.8
If the temperature of the Sun fell 5%, and the radius shrank 10%, what would be the percentage change of the Sun’s power output?
- 34%

10. Example 11.9 DATA: The sun radiates 3.74x1026 W
Distance from Sun to Earth = 1.5x1011 m
Radius of Earth = 6.36x106 m
What is the intensity (power/m2) of sunlight when it reaches Earth?
How much power is absorbed by Earth in sunlight? (assume that none of the sunlight is reflected)
What average temperature would allow Earth to radiate an amount of power equal to the amount of sun power absorbed?
a) 1323 W/m2
b) 1.68x1017 W
c) T = 276 K = 3 ºC = 37 ºF

11. What is neglected in estimate?
Earth is not at one single temperature
Some of Sun’s energy is reflected
Reduces TE ~ 20°K
Emissivity lower at Earth’s thermal wavelengths than at Sun’s wavelengths (due to atmosphere)
Increases TE ~ 40°K
Natural greenhouse effect - necessary for life on Earth
Radioactive decays inside Earth are additional
source of energy
Small effect for Earth
Jupiter radiates much more energy than it receives from the sun

12. Example 11.10a
Two Asteroids A and B orbit the Sun at the same radius R. Asteroid B has twice the surface area of A. (Assume both asteroids absorb 100% of the sunlight and have emissivities of 1.0)
The average temperature of B, TB = _____
a) (1/4)TA
b) (1/2)TA
c) TA
d) 2TA
e) 4TA

13. Example 11.10b a) (1/4)TA b) (1/2)TA c) (2-1/2)TA d) (2-1/4)TA e) TA
Two identical asteroids A and B orbit the sun. Asteroid B is located twice as far from sun as Asteroid A RB=2RA
(Assume both asteroids absorb 100% of the sunlight and have emissivities of 1.0)
The average temperature of B, TB = _____
a) (1/4)TA
b) (1/2)TA
c) (2-1/2)TA
d) (2-1/4)TA
e) TA

14. Example 11.10c a) (1/4)TA b) (1/2)TA c) (2-1/2)TA d) (2-1/4)TA
Two Asteroids A and B orbit the Sun at the same radius R. Asteroid B is painted with reflective paint which reflects 3/4 of the sunlight, while asteroid A absorbs 100% of the sunlight. Both asteroids have emissivities of 1.0.
The average temperature of B, TB = _____
a) (1/4)TA
b) (1/2)TA
c) (2-1/2)TA
d) (2-1/4)TA
e) (2-3/4)TA

15. Example 11.10d a) 4TA b) 2TA c) 21/2TA d) 21/4TA e) 23/4TA
Two Asteroids A and B orbit the Sun at the same radius R. Asteroid B has an emissivity of 0.25, while the emissivity of asteroid A is 1.0. Both asteroids absorb 100% of the sunlight.
The average temperature of B, TB = _____
a) 4TA
b) 2TA
c) 21/2TA
d) 21/4TA
e) 23/4TA

16. Greenhouse Gases
Sun is much hotter than Earth so sunlight has much shorter wavelengths than light radiated by Earth (infrared)
Emissivity of Earth depends on wavelength
CO2 in Earth’s atmosphere reflects in the infrared
Barely affects incoming sunlight
Reduces emissivity, e, of re-radiated heat

17. Global warming Tearth has risen ~ 1 ºF in past 100 years
“most of observed increase […] is very likely due to the observed increase in anthropogenic greenhouse gas concentrations” Intergovernmental Panel on Climate Change (IPCC)

18. Mercury and Venus
Tmercury = 700 K (day)
& 90 K (night)
Tvenus = 740 K