PHYSICS 231 INTRODUCTORY PHYSICS I Lecture 17
Heat: Q = Energy transferred due to microscopic contact Recap - Heat Transfer Heat can: Change temperature Q = mc!t c = specific heat For water: c= 1.0 cal/(g C) Change state of matter Q = ml L = Latent heat of fusion or vaporization For water: L F =79.7 cal/g, L V =540 cal/g
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
Rate of heat transfer Conduction P = Q t = ka " #T /#x = A " #T /R Conductivity k is property of material R = "x /k R-value also depends on thickness. It adds for layered objects (R=R 1 +R 2 )
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: k glass = 0.84 W/mºC, k air = 0.0234 W/m ºC P 1 /P 2 = 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.
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 P = e! AT 4 Emissivity, 0 < e < 1, usually near 1 T must be in Kelvin!!!! = 5.6696x10-8 W/(m 2 ºK 4 ) is the Stefan-Boltzmann constant
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 3.74x10 26 W Distance from Sun to Earth = 1.5x10 11 m Radius of Earth = 6.36x10 6 m a) What is the intensity (power/m 2 ) of sunlight when it reaches Earth? a) 1323 W/m 2 b) How much power is absorbed by Earth in sunlight? (assume that none of the sunlight is reflected) b) 1.68x10 17 W 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 ºC = 37 ºF
What is neglected in estimate? Earth is not at one single temperature Some of Sun s energy is reflected Reduces T E ~ 20 K Emissivity lower at Earth s thermal wavelengths than at Sun s wavelengths (due to atmosphere) Increases T E ~ 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, T B = a) (1/4)T A b) (1/2)T A c) T A d) 2T A e) 4T A
Example 11.10b Two identical asteroids A and B orbit the sun. Asteroid B is located twice as far from sun as Asteroid A. R B =2R A (Assume both asteroids absorb 100% of the sunlight and have emissivities of 1.0) The average temperature of B, T B = a) (1/4)T A b) (1/2)T A c) (2-1/2 )T A d) (2-1/4 )T A e) T A
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, T B = a) (1/4)T A b) (1/2)T A c) (2-1/2 )T A d) (2-1/4 )T A e) (2-3/4 )T A
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, T B = a) 4T A b) 2T A c) 2 1/2 T A d) 2 1/4 T A e) 2 3/4 T A
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 CO 2 in Earth s atmosphere reflects in the infrared Barely affects incoming sunlight Reduces emissivity, e, of re-radiated heat
Global warming T earth 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 T mercury = 700 K (day) & 90 K (night) T venus = 740 K