Lecture 24Purdue University, Physics 2201 Phase Diagram H2OH2O

Lecture 24Purdue University, Physics 2202 Boiling Point Going from Lafayette to Denver the temperature at which water boils: A) IncreasesB) DecreasesC) Same

Lecture 24Purdue University, Physics 2203 Exercise During a tough work out, your body sweats (and evaporates) 1 liter of water to keep cool (37 C). How much cold water would you need to drink (at 2 C) to achieve the same thermal cooling? (recall C V = 4.2 J/g for water, L v =2.2x10 3 J/g) A) 0.15 liters B) 1.0 litersC) 15 liters D) 150 liters Q evaporative = L m = 2.2x10 3 kJ/kg x 1kg Q c = c m  t = 4.2kJ/kgK x 35K x m m = 2.2x10 3 / 147 = 15kg or 15 liters!

Lecture 24Purdue University, Physics 2204 Exercise How much ice (at 0 C) do you need to add to 0.5 liters of a water at 25 C, to cool it down to 10 C? (L = 80 cal/g, c = 1 cal/g C)

Lecture 24Purdue University, Physics 2205 Exercise Ice cube trays are filled with 0.5 kg of water at 20 C and placed into the freezer. How much energy must be removed from the water to turn it into ice cubes at -5 C? (L = 80 cal/g, c water = 1 cal/g C, c ice = 0.5 cal/g C) Water going from 20 C to 0 C: Water turning into ice at 0 C: Ice going from 0 C to -5 C:

Lecture 25Purdue University, Physics 2206 Lecture 25 Heat Transfer PHYSICS 220

Heat transfer Conduction Convection Electro-magnetic radiation Lecture 25Purdue University, Physics 2207

Lecture 25Purdue University, Physics 2208 Heat Transfer: Conduction Hot molecules have more KE than cold molecules High-speed molecules on left collide with low-speed molecules on right – energy transferred to lower-speed molecules – heat transfers from hot to cold –vibrations

Lecture 25Purdue University, Physics 2209 Heat Transfer: Conduction I = rate of heat transfer = Q/t [J/s] I =  A (T H -T C )/d Q/t =  A  T/  x  = thermal conductivity Units: J/s*m*C good conductors…high  e.g., metal good insulators … low  e.g., plastic R = d/(A  = thermal resistance T H Hot T C Cold d =  x Area A

Lecture 25Purdue University, Physics Conduction Which of the following is an example of conductive heat transfer? A) You stir some hot soup with a silver spoon and notice that the spoon warms up. B) You stand watching a bonfire, but can’t get too close because of the heat. C) Its hard for central air-conditioning in an old house to cool the attic.

Lecture 25Purdue University, Physics Find I=Q/t in J/s Key Point: Continuity (just like fluid flow) I 1 = I 2  1 A(T 0 -T C )/  x 1 =  2 A(T H -T 0 )/  x 2 solve for T 0 = temp. at junction then solve for I 1 or I 2 T H -T 0 = I R 1 and T 0 -T C = I R 2  T = (T H -T 0 ) + (T 0 -T C ) = I (R 1 + R 2 )  x 1 = 0.02 m A 1 = 35 m 2 k 1 = J/s*m*C  x 2 = m A 2 = 35 m 2 k 2 = J/s*m*C answer: T 0 =2.27 C I=318 Watts Inside: T H = 25C Outside: T C = 0C I1I1 I2I2 T0T0 Conduction with 2 Layers

Lecture 25Purdue University, Physics Touch the metal base of a chair and the top of a wooden desk in an air-conditioned room, which feels colder? A) BaseB) SameC) Desk Both must be the same temperature (room temperature), but metal feels colder because it conducts heat better/faster. iClicker

Lecture 25Purdue University, Physics Heat Transfer: Convection Air heats at bottom Thermal expansion…density gets smaller Lower density air rises –Archimedes: low density floats on high density Cooler air pushed down Cycle continues with net result of circulation of air I = Q/t = h A  T h = coefficient of convection Practical aspects –heater ducts on floor –A/C ducts on ceiling –stove heats water from bottom

Lecture 25Purdue University, Physics Convection

Lecture 25Purdue University, Physics Convection Which of the following is an example of convective heat transfer? A) You stir some hot soup with a silver spoon and notice that the spoon warms up. B) You stand watching a bonfire, but can’t get too close because of the heat. C) Its hard for central air-conditioning in an old house to cool the attic.

Lecture 25Purdue University, Physics Convection

Lecture 25Purdue University, Physics Heat Transfer: Radiation All things radiate / absorb electromagnetic energy Why? - Because vibration or/and acceleration of charged particles (electrons, protons, ions) results in electromagnetic radiation and vice versa. No “medium” required How amount of emitted / absorbed radiation depends on body temperature?

Lecture 25Purdue University, Physics Heat Transfer: Radiation I emit = Q/t = eA  T 4 Stefan-Boltzmann Law e = emissivity (between 0 and 1) perfect “black body” has e=1 (What does it mean “black body”?) T is the temperature of the object (in Kelvin)  = Stefan-Boltzmann constant = 5.67 x J/s*m 2 *K 4 I absorb = eA  T 0 4 good emitters (e close to 1) are also good absorbers

Lecture 25Purdue University, Physics Question One day during the winter, the sun has been shining all day. Toward sunset a light snow begins to fall. It collects without melting on a cement playground, but it melts immediately upon contact on a black asphalt road adjacent to the playground. How do you explain this. The black asphalt absorbs more heat from the sun. The black asphalt has an emissivity of 1 and absorbs energy from the surrounding (from the sun) compared to a smaller number for the cement. As a result, it is at a higher temperature than the cement and melts the snow.

Lecture 25Purdue University, Physics All things radiate and absorb electromagnetic energy I emit = eA  T 4 I absorb = eA  T 0 4 I net = I emit - I absorb = eA  (T 4 - T 0 4 ) if T > T 0, object cools down if T < T 0, object heats up T Surroundings at T 0 Hot stove Heat Transfer: Radiation

Lecture 25Purdue University, Physics Exercise The Earth has a surface temperature around 270 K and an emissivity of 0.8, while space has a temperature of around 2 K. What is the net power radiated by the earth into free space? (Radii of the Earth and the Sun are R E = 6.38×10 6 m, R S = 7×10 8 m.) I net = I emit - I absorb = eA  (T 4 - T 0 4 )

Lecture 25Purdue University, Physics Radiation Which of the following is an example of radiative heat transfer? A) You stir some hot soup with a silver spoon and notice that the spoon warms up. B) You stand watching a bonfire, but cant get too close because of the heat. C) Its hard for central air-conditioning in an old house to cool the attic.

Lecture 25Purdue University, Physics iClicker Amount of radiation emitted by the Earth is A) less B) equal C) more (than) the amount of radiation absorbed by the Earth from the Sun.

Lecture 25Purdue University, Physics Radiation Spectrum Wien’s Law: max T = × mK Infrared: 100  m  m Visible Light: 0.7  m-0.4  m Ultraviolet: < 0.4  m (stars which are hotter than sun) How frequency of radiation depends on T?

Night vision goggles Lecture 25Purdue University, Physics 22025

Lecture 25Purdue University, Physics Temperature of the Sun The Sun appear yellowish, i.e.,  = 0.5  m. What is the temperature at the surface of the Sun? m T = x m K T = x / 0.5 x = 6000 K