# PHYSICS 231 INTRODUCTORY PHYSICS I Lecture 17

```PHYSICS 231
INTRODUCTORY PHYSICS I
Lecture 17
Recap - Heat Transfer
•
Heat: Q = Energy transferred due to microscopic
contact
•
Heat can:
•
•
Change temperature
Q  mcT
•
c = specific heat
•
For water: c= 1.0 cal/(g&deg;C)
Change state of matter
Q  mL
•
L = Latent heat of fusion or vaporization
•
For water: LF=79.7 cal/g, LV=540 cal/g
Example 11.11
A 50 g ice cube at 0&ordm;C is put into a styrofoam cup
containing 300 g of coffee at 90&ordm;C. 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&deg;C
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
• Energy transferred by light (UV, IR,…)
• Examples: Stars, Incandescent bulbs
Conduction
• Rate of heat transfer
Q
P   kA T /x
t
 A  T / R
• Conductivity k is property of
material
• R-value R  x /k also depends
layered objects (R=R1+R2)

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/m&ordm;C, kair= 0.0234 W/m &ordm;C
P1/P2 = 4.59
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.
• All objects emit light if T &gt; 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
P  e AT
Emissivity,
0 &lt; e &lt; 1, usually near 1
4
 = 5.6696x10-8 W/(m2&ordm;K4)
is the Stefan-Boltzmann
constant
T must be in Kelvin !!!
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%
Example 11.9
DATA: The sun radiates 3.74x1026 W
Distance from Sun to Earth = 1.5x1011 m
Radius of Earth = 6.36x106 m
a) What is the intensity (power/m2) of sunlight
a) 1323 W/m2
when it reaches Earth?
b) How much power is absorbed by Earth in
sunlight? (assume that none of the sunlight is
b) 1.68x1017 W
reflected)
c) What average temperature would allow Earth to
radiate an amount of power equal to the amount
of sun power absorbed?
c) T = 276 K = 3 &ordm;C = 37 &ordm;F
What is neglected in estimate?
•Earth is not at one single temperature
•Some of Sun’s energy is reflected
•Reduces TE ~ 20&deg;K
•Emissivity lower at Earth’s thermal wavelengths
than at Sun’s wavelengths (due to atmosphere)
•Increases TE ~ 40&deg;K
•Natural greenhouse effect - necessary for
life on Earth
source of energy
•Small effect for Earth
•Jupiter radiates much more energy than it
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)
b)
c)
d)
e)
(1/4)TA
(1/2)TA
TA
2TA
4TA
Example 11.10b
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)
b)
c)
d)
e)
(1/4)TA
(1/2)TA
(2-1/2)TA
(2-1/4)TA
TA
Example 11.10c
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)
b)
c)
d)
e)
(1/4)TA
(1/2)TA
(2-1/2)TA
(2-1/4)TA
(2-3/4)TA
Example 11.10d
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)
b)
c)
d)
e)
4TA
2TA
21/2TA
21/4TA
23/4TA
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,