THERMAL PHYSICS NOTES

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1 THERMAL PHYSICS NOTES PHYSICS B4B BAKERSFIELD COLLEGE Rick Darke (Instructor)

2 THERMODYNAMICS TERMS thermodynamics - that branch of physics which deals with heat and temperature (also called thermal physics) system - a definite quantity of matter enclosed by boundaries (real or imaginary) open system - a system, into or out of which mass may be transferred closed system - a system for which there is no transfer of mass across the boundaries

3 THERMODYNAMICS TERMS temperature - an index of the average random translational kinetic energy of particles in a system; a relative measure of hotness or coolness heat (energy) - the energy exchanged between objects because of a difference of temperature; a measure of the random kinetic energy of molecules in a substance thermal contact - a condition in which heat may be exchanged between two objects

4 THERMODYNAMICS TERMS thermal equilibrium - the condition in which there is no net heat exchange between objects in thermal contact thermally isolated system - a system for which there is no transfer of heat energy across its boundaries completely isolated system - a system for which there is no transfer of mass or heat energy across its boundaries (thermally isolated and closed)

5 HOW TO MAKE A THERMOMETER STEP 1: Obtain a thermometric substance with some temperature response you believe to be a linear function of temperature. example: liquid mercury. The volume of the mercury is a function of its temperature, and in a capillary of fixed diameter, the volume changes in mercury will be observable as height changes in the mercury column.

6 HOW TO MAKE A THERMOMETER STEP 2: Create a temperature scale by defining two fixed-point temperatures. example: Define the temperature of a water-ice equilibrium system at 1.0 atm to be 0 C. Define the temperature of a water-steam equilibrium system at 1.0 atm to be 100 C. 100 C 0 C

7 HOW TO MAKE A THERMOMETER STEP 3: Create a graduated scale by dividing the interval between the fixedpoint temperatures linearly into a number of divisions. This graduated scale can then be extrapolated in both directions from the two fixed-point temperatures. 100 C 80 C 60 C 40 C 20 C 0 C

8 P(atm) PHASE DIAGRAM OF H 2 O vaporifusion liquid zation curve (water) curve solid triple (ice) point.006 sublimation gas curve (steam) T( C)

9 DEFINITION OF THE KELVIN 1 kelvin (S.I. unit of temperature) = 1/ of the thermodynamic temperature of the triple-point of H 2 O (P = 0.61 kpa and T = 0.01 C) note: You must use kelvin temperatures in all expressions in which the (absolute) temperature T is involved, but you may use either kelvins or degrees celsius in expressions in which temperature difference ΔT is involved. examples: P = σeat 4 must use kelvins Q = mcδt may use kelvins or C

10 TEMPERATURE SCALES scale absolute? conversions Kelvin yes T K = T C Rankine yes T R = T F Celsius no T C = (T F - 32)(5/9) Fahrenheit no T F = 1.8T C

DON HERBERT (MR. WIZARD) Donald Jeffry Herbert (7-10-1917 to 6-12-2007) was the creator and host of the shows "Watch Mr. Wizard" (1951-65, 1971-72) and "Mr.

11 DON HERBERT (MR. WIZARD) Donald Jeffry Herbert ( to ) was the creator and host of the shows "Watch Mr. Wizard" ( , ) and "Mr. Wizard's World" ( ), educational television programs for children devoted to science and technology. He also produced many short video programs about science and authored several popular books about science for children.

12 ABSOLUTE ZERO EXPERIMENT DATA bath T ( C) P (psia) dry ice + alcohol room air boiling water ice water

13 ABSOLUTE ZERO EXPERIMENT GRAPH P (psia) T ( C)

14 ZEROTH LAW OF THERMODYNAMICS If two systems A and B are in thermal equilibrium with a third system C, then they will be in thermal equilibrium with each other if placed in thermal contact. Two objects in thermal equilibrium with each other are at the same temperature. system A system B system A no net heat flow and no net heat flow no net heat flow system C system C system B

15 LINEAR EXPANSION COEFFICIENTS material α at 20 C ( C -1 ) aluminum 24 x 10-6 brass 19 x 10-6 copper 17 x 10-6 concrete 12 x 10-6 steel 11 x 10-6 glass (ordinary) 9.0 x 10-6 glass (pyrex) 3.2 x 10-6 invar (Ni-Fe alloy) 0.9 x 10-6

16 VOLUME EXPANSION COEFFICIENTS material β at 20 C ( C -1 ) air 37 x 10-4 gasoline 9.6 x 10-4 glycerine 4.9 x 10-4 mercury 1.8 x 10-4 acetone 1.5 x 10-4 ethanol 1.1 x 10-4

17 PHASE CHANGE TERMS freezing condensing ice water steam melting boiling sublimating resublimating

THERMAL EXPANSION PROBLEM A copper sphere has a diameter of 2.000 cm and is at room temperature (20 C).

18 THERMAL EXPANSION PROBLEM A copper sphere has a diameter of cm and is at room temperature (20 C). An aluminum plate has a circular cut-out with a diameter of cm (also at room temperature). At what (common) temperature would the copper sphere just barely be able to pass through the hole in the aluminum plate?

19 THERMAL EXPANSION PROBLEM A steel rod of circular cross-section and diameter 5.0 cm spans a 2.5-meter gap between two concrete fixtures. At 20 C the beam is not compressed and just touches each of the fixtures. What force is exerted on the fixtures when the temperature of the steel beam rises to 80 C (but the distance between the fixtures does not change)? The Young's modulus of steel is 2.0x10-6 Pa.

20 IDEAL GAS LAW PROBLEM How many moles of carbon dioxide would there be in a 3.5-cm 3 CO 2 cartridge at room temperature (20 C) if the gauge pressure of the gas in the cartridge is 500 psi? How many molecules of carbon dioxide would there be in the cartridge?

21 IDEAL GAS LAW PROBLEM An aerosol can contains a gas whose gauge pressure is 2.0 atm at 22 C. Suppose that the can will rupture when the gauge pressure of the gas inside rises to 3.5 atm. If the can were tossed into a fire, at what temperature will the can rupture?

22 IDEAL GAS LAW PROBLEM 66.0 ft 3 of air at atmospheric pressure and at 22 C is to be placed into a 10.0-liter scuba tank. Just after this transfer, it is found that the tank's gauge shows a pressure of 3000 psig. What temperature is the air immediately after the tank is filled?

23 IDEAL GAS LAW PROBLEM A bubble is released from the bottom of a fresh-water lake, 15.0 meters below the surface. The gas in the bubble is 4 C when released and warms to 20 C by the time it reaches the surface. If the bubble had a volume of 2.0 cm 3 at release, what will be its volume when it reaches the surface?

24 HEAT ENERGY UNITS calorie: the amount of heat energy required to raise the temperature of 1 gram of water from 14.5 C to 15.5 C (also called the "15-degree calorie" or the "little calorie") Calorie: 1000 calories (also called the kilocalorie [kcal] or the "big calorie") Btu (British thermal unit): the amount of heat energy required to raise the temperature of 1 pound of water from 63 F to 64 F

25 MECHANICAL EQUIVALENT OF HEAT mechanical equivalent of heat (MEH): the conversion factor between mechanical energy and heat energy: 1 cal = J 1 Cal = 4186 J 1 Btu = 1055 J

JOULE'S EXPERIMENT In 1845 British physicist James Joule presented the paper "On the Mechanical Equivalent of Heat" to the British Association meeting in Cambridge.

26 JOULE'S EXPERIMENT In 1845 British physicist James Joule presented the paper "On the Mechanical Equivalent of Heat" to the British Association meeting in Cambridge. In this work he reported the results of his best-known experiment, in which he estimated the mechanical equivalent of heat to be 819 ft lbf/btu (4.41 J/cal). In 1850, Joule obtained a refined measurement of 773 ft lbf/btu (4.16 J/cal).

JOULE'S APPARATUS Joule's apparatus employed a falling weight, in which gravity does the mechanical work in spinning a paddle-wheel in an insulated

27 JOULE'S APPARATUS Joule's apparatus employed a falling weight, in which gravity does the mechanical work in spinning a paddle-wheel in an insulated barrel of water. The temperature of the water is increased through the viscous dissipation of mechanical energy which is converted into heat energy.

28 SPECIFIC HEATS material c (J/kg. C) c (cal/g. C) aluminum brass copper iron lead glass ice water steam ethanol

29 LATENT HEATS (FUSION) material M.P. ( C) L f (J/kg) L f (cal/g) H 2 O 0 333, aluminum , copper , lead , ethanol , sulfur , helium ,

30 LATENT HEATS (VAPORIZATION) material B.P. ( C) L v (J/kg) L v (cal/g) H 2 O 100 2,260, aluminum ,400, copper ,060, lead , ethanol , sulfur , helium ,

31 HEAT ENERGY PROBLEM At Vernal Falls in Yosemite National Park, California, water in the Merced River plummets 97 meters from the rim of the falls to a pool below. What is the temperature increase of the water after dropping this distance? Hint: You need to consider two energy conversions.

32 HEAT ENERGY PROBLEM Compute the amount of heat energy required to convert 10 grams of ice originally at -20 C to steam at 150 C?

33 CALORIMETRY PROBLEM A styrofoam cup contains 100 grams of water at 50 C. A 40- gram piece of ice at -20 C is placed in the cup, and the system is allowed to come to thermal equilibrium. Assuming the cup does not take part in any heat sharing, describe thermal equilibrium reached by the system.

34 CALORIMETRY PROBLEM A styrofoam cup contains 100 grams of water at 60 C. A 200- gram piece of ice at -40 C is placed in the cup, and the system is allowed to come to thermal equilibrium. Assuming the cup does not take part in any heat sharing, describe thermal equilibrium reached by the system.

35 CALORIMETRY PROBLEM A styrofoam cup contains 100 grams of water at 20 C. A 200- gram piece of ice at -60 C is placed in the cup, and the system is allowed to come to thermal equilibrium. Assuming the cup does not take part in any heat sharing, describe thermal equilibrium reached by the system.

36 THERMODYNAMIC PROCESSES A process is a continuous change in the state of a material. If the material is a gas, it is usual to consider P as a function of V (with temperature suppressed) in graphing the process (PV-diagram). An arrow is used to make the time-progression of the process obvious. P 1 P 2 P V 1 V 2 V

37 FIRST LAW OF THERMODYNAMICS The infinitesimal increase in internal energy (de) of a system is accounted for by the infinitesimal amount of heat energy (dq) transferred (added) to the system and the infinitesimal amount of work (dw) done on the system by the environment. de = dq + dw = dq - PdV dw dq de

38 FIRST LAW OF THERMODYNAMICS The increase in internal energy (ΔE 12 ) of a system taken through a process from state 1 to state 2 is accounted for by the amount of heat energy (Q 12 ) transferred (added) to the system during the process and the amount of work (W 12 ) done on the system by the environment during the process. 2 ΔE 12 = Q 12 + W 12 = Q 12 - S PdV 1 W 12 Q 12 ΔE 12

39 ISOBARIC PROCESS A process throughout which the system pressure remains constant (P = constant or dp = 0). Q 12 = (ν/2 + 1)PΔV W 12 = - PΔV ΔE 12 = (ν/2)pδv P P or you can substitute nrδt for PΔV in the above V 1 V 2 V

40 ISOCHORIC PROCESS A process throughout which the system volume remains constant (V = constant or dv = 0). P 1 P Q 12 = (ν/2)vδp W 12 = 0 ΔE 12 = (ν/2)vδp or you can substitute nrδt for VΔP in the above P 2 V V

41 ISOTHERMAL PROCESS A process throughout which the system temperature remains constant (T = constant or dt = 0). P 1 P Q 12 = PVln(P 2 / P 1 ) W 12 = - PVln(P 2 / P 1 ) ΔE 12 = 0 or you can substitute nrt for PV or V 1 /V 2 for P 2 /P 1 in the above P 2 V 1 V 2 V

42 ADIABATIC PROCESS A process throughout which the system does not absorb or expel heat energy (Q 12 = 0 or dq = 0). P 1 P Q 12 = 0 W 12 = (ν/2)δ(pv) ΔE 12 = (ν/2)δ(pv) or you can substitute nrδt for Δ(PV) in the above P 2 V 1 V 2 V

43 PROCESSES FOR IDEAL GASES process Q W ΔE general (ν/2)δ(pv)+spdv -SPdV (ν/2)δ(pv) isobaric (ν/2+1)pδv -PΔV (ν/2)pδv (dp = 0) nc P ΔT -nrδt nc V ΔT isochoric (ν/2)vδp 0 (ν/2)vδp (dv = 0) nc V ΔT 0 nc V ΔT isothermal PVln(P 2 /P 1 ) -PVln(P 2 /P 1 ) 0 (dt = 0) nrtln(p 2 /P 1 ) -nrtln(p 2 /P 1 ) 0 adiabatic 0 (ν/2)δ(pv) (ν/2)δ(pv) (dq = 0) 0 nc V ΔT nc V ΔT

44 FIRST LAW PROBLEM Calculate the increase in internal energy of 1.0 gram of H 2 O when it is taken from water at 100 C to steam at 100 C (assume that the process occurs at atmospheric pressure). H 2 O (g) H 2 O (l)

45 ISOBARIC PROCESS PROBLEM Calculate the increase in internal energy of 1.0 gram of H 2 O when it is taken from water at 100 C to steam at 100 C (assume that the process occurs at atmospheric pressure). H 2 O (g) H 2 O (l)

46 ISOCHORIC PROCESS PROBLEM Calculate the increase in internal energy of 1.0 gram of H 2 O when it is taken from water at 100 C to steam at 100 C (assume that the process occurs at atmospheric pressure). H 2 O (g) H 2 O (l)

47 ISOTHERMAL PROCESS PROBLEM Calculate the increase in internal energy of 1.0 gram of H 2 O when it is taken from water at 100 C to steam at 100 C (assume that the process occurs at atmospheric pressure). H 2 O (g) H 2 O (l)

ADIABATIC PROCESS PROBLEM During the upstroke of the handle of a bicycle pump, air at a temperature of 20 C enters a 0.75-L volume of the cylinder (at 1.0 atm).

48 ADIABATIC PROCESS PROBLEM During the upstroke of the handle of a bicycle pump, air at a temperature of 20 C enters a 0.75-L volume of the cylinder (at 1.0 atm). A quick downstroke compresses the air to a volume of 0.15 L. Assuming that no heat energy flows out through the cylinder wall, find the temperature of the air in the cylinder immediately after the compression. Take γ for air to be 1.40.

49 CUSTOM PROCESS PROBLEM Calculate the increase in internal energy of 1.0 gram of H 2 O when it is taken from water at 100 C to steam at 100 C (assume that the process occurs at atmospheric pressure). H 2 O (g) H 2 O (l)

50 THERMAL CONDUCTIVITY The rate P at which heat is conducted through a slab of material (W or Btu/h) with cross-sectional area A and thickness L whose faces are maintained at temperatures T H and T C is given by: P = ka(t H - T C )/L where k is the thermal conductivity of the material of the slab (measured in W/m. C or Btu/ h. ft. F). T H L A T C

51 THERMAL CONDUCTIVITIES substance k (W/m.o C) substance k (W/m.o C) silver 427 water 0.6 copper 397 rubber 0.2 gold 314 hydrogen 0.17 aluminum 238 helium 0.14 iron 80 asbestos 0.08 ice 2 wood concrete 0.8 oxygen glass 0.8 air 0.023

52 R-VALUES substance and thickness R-value (ft 2. F. h/btu) drywall (0.5" thick) 0.45 glass pane (1/8" thick) 0.89 insulating glass (1/4") 1.54 concrete block (filled cores) 1.93 brick (4" thick) 4.00 styrofoam (1" thick) 5.00 fiber glass (3.5" thick) 10.9 fiber glass (6" thick) 18.8

53 THERMAL CONDUCTIVITY PROBLEM A pane of glass is 1/8" thick and has dimensions 1.5 m by 2.5 m. It separates two heat reservoirs whose temperatures are 10 C and 22 C. What is the rate of heat transport through the pane?

54 THERMAL CONDUCTIVITY PROBLEM 90 C insulator Cu Al insulator 15 C A copper and an aluminum cylinder are joined end-to-end as shown. Each has a diameter of 4.0 cm and a length of 25.0 cm. One end of the copper cylinder is maintained at 90 C and one end of the aluminum cylinder is maintained at 15 C. What is the junction temperature?

THERMAL RADIATION The rate P of radiant energy loss (watts) from the surface of an object with surface area A and surface temperature T is given by: P = σaet 4 where σ is

55 THERMAL RADIATION The rate P of radiant energy loss (watts) from the surface of an object with surface area A and surface temperature T is given by: P = σaet 4 where σ is the Stefan-Boltzmann constant (5.67x10-8 W/m 2. K 4 ), and e is the emissivity of the surface of the object (dimensionless parameter). This is called the Stefan-Boltzmann Law.

56 THERMAL RADIATION PROBLEM The surface of a cube with sides of length 0.05 m has an emissivity of If the surface of the cube is maintained at a temperature of 550 C, what is the radiant energy flux through the surface of the cube?

57 MOLAR SPECIFIC HEATS (J/mol. K) gas C P C V γ = C P /C v He Ar H N O CO H CH

58 SECOND LAW OF THERMODYNAMICS It is impossible to construct a heat engine that, operating in a cycle, produces no effect other than the input of energy by heat from a reservoir and the performance of an equal amount of work (Kelvin-Planck formulation). It is impossible to construct a cyclical machine whose sole effect is to transfer energy continuously by heat from one object to another at a higher temperature without the input of energy by work (Clausius statement).

59 ENTROPY Entropy (S) is a quantity describing the disorder of a system. It has dimensions of heat energy per temperature (cal/k or J/K). It is equal to the Boltzmann constant (k B ) times the natural log of the total number of ways (W) in which the system can arrange itself consistent with energy being conserved. S = k B lnw

60 ENTROPY Entropy is an extensive physical quantity. The total entropy of a system is equal to the sum of the entropies of each of the system's components. n S total = Σ S i i=1

61 ENTROPY CHANGE Calculating the entropy change ΔS for a system is usually a more tractable problem than calculating the entropy itself. The change in entropy of a system taken through a process from state 1 to state 2 is most often derivable from 2 ΔS 12 = S 2 - S 1 = S dq/t 1

62 ENTROPY CHANGE warming: In changing the temperature of a material from T 1 to T 2 without changing its phase, use: ΔS 12 = mcln(t 2 /T 1 ) or ncln(t 2 /T 1 ) example: Find the change in entropy of a 250-gram piece of copper heated from 20 o C to 180 o C. Take the specific heat of copper to be.092 cal/g.o C.

63 ENTROPY CHANGE phase change: In changing the phase of a material without changing its temperature, use: ΔS Δ phase = + ml/t example: Find the change in entropy of a 1.5-kg mass of water (initially at 0 o C) when it is fully frozen, producing ice at 0 o C. Take the latent heat of fusion for H 2 O to be 2.26 x 106 J/K.

64 ENTROPY CHANGE free expansion: In allowing a gas to free-expand from initial volume V 1 to final volume V 2, use: ΔS 12 = nrln(v 2 /V 1 ) example: Find the change in entropy when an ideal gas at 1.0 atm and 20 o C occupying a chamber whose volume is 0.5 m3 is allowed to free-expand into an evacuated chamber whose (extra) volume is 2.5 m3.

65 ENTROPY CHANGE mixing of gases: In mixing n A moles of gas A, initially occupying volume V A, with n B moles of gas B, initially occupying volume V B : ΔS 12 = n A Rln([V A + V B ]/V A ) + n B Rln([V A + V B ]/V B ) example: A chamber is divided into two compartments separated by a partition. Compartment A (H 2 gas): V =.75 m 3, P = 1.0 atm, and T = 30 o C. Compartment B (CO 2 gas): V =.25 m 3, P = 1.0 atm, and T = 30 o C. The partition is removed and the gases mix. Find the change in entropy of the system.

66 ENTROPY PROBLEM A 60-gram piece of ice at 0 o C is placed in a container with 200 grams of water at 50 o C. Find the temperature of this system after thermal equilibrium is attained. Use this result to find ΔS for: (1) the water; (2) the ice; and (3) the entire system during this process. Assume that the container does not transfer any heat energy.

THERMAL PHYSICS NOTES

THERMAL PHYSICS NOTES PHYSICS B4B BAKERSFIELD COLLEGE Rick Darke (Instructor) THERMODYNAMICS TERMS thermodynamics - that branch of physics which deals with heat and temperature (also called thermal physics)