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 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 C is put into a styrofoam cup containing 300 g of coffee at 90 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 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 Q P kA T x t A T R Conductivity k is property of material R value R x k also depends on thickness It adds for 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 C kair 0 0234 W m 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 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 Emissivity 0 e 1 usually near 1 4 5 6696x10 8 W m2 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 when it reaches Earth a 1323 W m2 b How much power is absorbed by Earth in sunlight assume that none of the sunlight is reflected b 1 68x1017 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 C 37 F 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 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 of re radiated heat Global warming Tearth has risen 1 F 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
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