PHYSICS 231

INTRODUCTORY PHYSICS I

PHYSICS 231

INTRODUCTORY PHYSICS I

Lecture 17

• 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

Recap - Heat Transfer

Q =mcΔT

Q =mL

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

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

Conduction

• Rate of heat transfer

• Conductivity k is property ofmaterial

• R-value also dependson thickness. It adds for layered objects (R=R1+R2)

€

P =Q

t= kA ⋅ΔT /Δx

= A ⋅ΔT /R

€

R = Δx /k

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= 0.0234 W/m ºC

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.

P =eσAT 4

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

σ = 5.6696x10-8 W/(m2ºK4)is the Stefan-Boltzmann constant

Emissivity, 0 < e < 1, usually near 1

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 when it reaches Earth?

b) How much power is absorbed by Earth in sunlight? (assume that none of the sunlight is reflected)

c) 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

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

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

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) (1/4)TA

b) (1/2)TA

c) (2-1/2)TA

d) (2-1/4)TA

e) 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) (1/4)TA

b) (1/2)TA

c) (2-1/2)TA

d) (2-1/4)TA

e) (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) 4TA

b) 2TA

c) 21/2TA

d) 21/4TA

e) 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, of re-radiated heat

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)

Mercury and Venus

Tmercury = 700 K (day) & 90 K (night)

Tvenus = 740 K