Chapter 10 Some Vocabulary Thermodynamics Study of energy transfers engines Changes of state solid liquid gas Thermal Physics Temperature and Heat Heat Transfer of microscopic thermal energy Thermal Equilibrium Condition after two objects are in thermal contact and finish exchanging heat 1 2 Zeroth Law of Thermodynamics Thermometers If A is in thermal equilibrium with B and B is in thermal equilibrium with C A is in thermal equilibrium with C Exploit temperature sensitivity of volume or length pressure electric resistance allows definition of temperature color objects at thermal equilibrium have same T average particle speeds Heat moves from high T to low T objects 3 4 Temperature Scales Absolute Temperature Celsius Kelvin Scale Water freezes at 0 C boils at 100 C Farenheit Water freezes at 32 F boils at 212 F T in C T in K 273 15 9 T in F 32 T in C 5 5 T in C T in F 32 9 Lowest possible energy at T 0 K Energy minimized at T 0 Ideal gas law only makes sense for absolute scale 5 6 Some Temperatures Thermal Expansion Lowest laboratory T 10 7 K At high T increased molecular vibration pushes molecules further apart At RHIC T 1013 K In big bang T 1040 K or more L T L0 Coefficient of Linear Expansion Property of Material 7 Area and Volume Expansion 8 Example 10 1 Each dimension length width height stretch The coefficient of volume expansion of water at 20 C is 2 07x10 4 K 1 If the average depth of the ocean is 4000 m by what height would the oceans rise due to thermal expansion if Earth s temperature rises by 2 C 1 65 m L T L0 A T 2 A0 V T 3 V0 If you live on a beach where the slope of the beach is one meter height per 100 meters how much of your beach would disappear 165 m warming doesn t go to all depths land also expands 9 10 Application Bimetallic Strip Global Warming http www ncdc noaa gov oa climate globalwarming html T rose 0 6 C in last 100 years T rose 0 25 C in last 25 years Expected to rise from 1 5 to 4 C by 2100 years Should rise higher in mid upper latitudes Sea levels rise 1 2 mm per year in last 100 years may rise from 10 cm to 90 cm by 2100 Melting Antarctic ice caps are important Used in thermostats 11 12 Water is Weird Ideal Gas Law For sufficiently dilute gas pressure is proportional to number proportional to temperature inversely proportional to volume PV nRT pressure volume Density INCREASES between 0 C and 4 C Maximum density of water is 1000 kg m3 at 4 C Density of ice 917 kg m3 Ice floats temperature Ideal Gas Constant number of moles 13 Ideal Gas Law 14 Microscopic Perspective PV nRT PV Nk BT One mole is NA 6 023x1023 molecules number of 12C atoms in 12 g of 12C R 8 31 N m mole K number of molecules 15 Example 10 2 Boltzmann s constant k 1 38x10 23 N m K R 6 023x1023 16 Example 10 3 Pure helium gas is admitted into a leak proof cylinder containing a movable piston The initial volume pressure and temperature of the gas are 15 L 2 0 atm and 300 K A vertical cylinder of crosssectional area 40 cm2 is fitted with a tight fitting frictionless piston of mass 50 0 kg see figure If the volume is decreased to 12 L and the pressure increased to 3 5 atm find the final temperature of the gas Assume helium behaves as an ideal gas If there is 0 15 mol of an ideal gas in the cylinder at 500 K determine the height h at which the piston will be in equilibrium under its own weight h 69 5 cm 420 K 17 18 Derivation Kinetic Theory of Gases We wish to show P 3 PV E 2 N px A t px 2mvx 2d t vx Area d2 1 px v2 1 2 m x mvx2 KEone part A t dA V 3V PV 2 KEall part s 3 19 Molecular Interpretation of Temperature Speed of Molecules Using KE 3 2 PV PV NkT 3 Nk BT 2 3 k BT 2 The root mean square rms speed of molecules is KE 1 2 mv 2 20 kB 1 38x10 23 1 2 3 mv k BT 2 2 J K vrms 3 kB T m 3RT M Lighter molecules move faster Temperature is proportional to the average kinetic energy of a single molecule 21 22 Internal Energy Example 10 4 In a monatomic gas the translational K E is the only type of energy the molecules can have A cylinder contains a mixture of helium 4He and argon 40Ar gas in equilibrium at a temperature of 150 C DATA mproton 1 67x10 27 kg U 3 nRT 2 a What is the average kinetic energy of each type of molecule 8 76x10 21 J U is the internal energy of the gas b What is the rms speed of each type of molecule He 1 62 km s Ar 512 m s In a polyatomic gas one also has rotational and vibrational energy 3 2 bigger number 23 24 Example 10 5a Example 10 5b Consider the cylinder on the right which is filled with an ideal gas Consider the cylinder on the right which is filled with an ideal gas If P is doubled while maintaining the same volume the r m s speed of the molecules must change by a factor of If P is doubled while maintaining the same volume T must change by a factor of a b c d e 1 2 21 2 2 4 Can not determine a b c d e 25 Example 10 5c Consider the cylinder on the right which is filled with an ideal gas If T is doubled while letting the piston slide freely the volume will change by a factor of a b c d e 1 2 21 2 2 4 Can not determine 27 1 2 21 2 2 4 Can not determine 26
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