T (K or C) Q (quant.) Phase change. (quant.) C T. Temperature change 14-0
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1 T (K or C) G L S Q Q (quant.) Phase change Q (quant.) C T Temperature change 14-0
2 Temperature How do we keep track of energy when it is distributed over many, many [~10 23 ] objects that are constantly exchanging energy? Temperature is a measure of the average energy per molecule. Measure o K : o C : o F High average speed High energy per molecule High T Low average speed Low energy per molecule Low T
3 Heat & Mechanical Work (background) In the 18 th century, some erroneously believed that an object certain amount of heat fluid or caloric that could flow from one place to another. Benjamin Thomas ( ) A.K.A Count Rumford observed the heat generated from the boring of cannon barrels by large drills. James Prescott Joule ( ) quantitatively measured the increased temperature done by mechanical energy. James Joule s Experiment => Energy is Conserved 14-2
4 Establishing Thermal Equilibrium Definition: Heat is the energy transferred between objects due to a temperature difference. Separated, but in thermal contact In Thermal Contact after a long period A < Q B A B T c colder T h hotter T (in thermal Equilibrium) T c < T < T h Equilibrium established by heat flow, Q, from hotter to colder system Zero th Law of Thermo If A is in thermal equilibrium with B, and C is also in thermal equilibrium with B, then A and C will be in thermal equilibrium if brought into thermal contact. temperature is a universal function 14-3
5 Energy Transfer Processes Convection: hot fluid/gas moves hot & cold material change places (most efficient transport mechanism) aside Physics of Storm formation Heating buildings Heat transport in Earth s mantle Source of volcanoes Primary cooling of electronics Earth Mantle 14-4
6 Energy Transfer Processes aside Conduction: no material motion Heat is transferred via atoms and electrons exchanging kinetic energy via collisions with adjacent atoms/electrons. Faster Internal Motions Slower Internal Motions Electrons most efficient. Conduction is strong in metals (e.g. copper, Pt, Au, Fe) and least effective in insulators. [actually wrought iron is not so good- pokers for fires] 14-5
7 aside 14-6
8 Retarding Energy Transfer Which feature of the thermos bottle or cryogenic container is responsible for insulating against each of the heattransfer processes? Vacuum cuts conduction and convection Silvered faces reflect radiation cuts radiation 14-7
9 Back to temperature Temperature Benchmarks Sun (center) 10 6 Sun (surface) 6000 light bulb 4000 hot stove 2000 Kelvin (k) O C O F H 2 O boils H 2 O freezes CO 2 sublimes N 2 boils N 2 freezes 44 He boils 4.2 Absolute Zero K scale 0= temperature where all motion stops (KE=0) 14-8
10 14-9
11 The Kelvin Scale The most grown-up (i.e. physicist s) temperature scale The pressure in a gas is proportional to its temperature. P gas 3 gas 2 gas T C While each gas has a different proportionality (slope), all reach zero pressure at the exact same temperature. This value is called Absolute Zero and the Kelvin Scale is identical to the Celsius scale minus degrees
12 energy 14-11
13 14-12
14
15 Thermal Expansion Most substances expand when heated in proportion to the change in temperature
16 From our definition: L = L 0 t where - thermal expansion coefficient L - L 0 = L 0 T L = L 0 [1 + (T - T0)] Ex: Verrazano-Narrows Bridge (Center Span) L 0 = 1300 m T ~ 100 O C Ex: Thermal Expansion stress = 12x10-6 m/ O C Designed for 120 O F - (-60 O F) =180 O F L = (1300 m)(12x10-6 )(100) = 1.56 m 14-15
17 The Thermostat Glass vial with mercury Bimetals with different thermal expansions. e.g. brass - steel When Hot When Cold Dial Bimetal Coil The glass vial containing mercury acts as the switch. When the vial gets tipped horizontally, the mercury makes electrical contact, starting the home heating system
18 ΔQ heat input in = + direction Define heat capacity (property of system) ΔQ C= ΔT system observe change in temperature The larger the system the larger the C (heat capacity). define specific heat c that a material property. mass C heat c= [J/kg K = J/kg O C] capacity C = c m m specific heat ΔT ΔQ = CΔT [J/K = J/ O C] ΔQ = m c ΔT specific heat
19 H 2 O standard ΔQ cal c(h2o) = 1 g o C c(h2o) 14-12a 14-18
20 Example Suppose 69.4 J is added to kg of a metal M. By how much does the temperature rise? ΔQ = m c ΔT M= Al ΔQ 69.4 J o ΔT = = K o m c (0.121 kg)(900 J/kg K) ΔT = ΔQ m c M= Pb ΔQ 69.4 J o ΔT = = 4.48 K o m c (0.121 kg)(128 J/kg K) Same mass fewer atoms (greater mass per atom) 14-12b 14-19
21 A Pb ball is dropped from h=5.43 m. Once the ball has come to rest on the floor by how much has the temperature increased? initial PE = mgh h KE = m 2 v 2 Q T Just before impact Later after impact (at rest energy trans. to heat) PE KE Q = m c T m g h = m c T o g h 9.8 (5.43) m/s (m) kg m /s K o T = = K o c 128 J/kg K J 14-20
22 14-21
23 14-22 Ar
24 14-23
25 PE dominates (molecularattraction) Low: v, KE Low T 14-add-1 PE important intermediate v, E PE un-important high: v, KE Low T High T
26 14-25
27 14-26
28 14-27
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