Announcements 5 Nov 2009 Temperature scales 1 Exam solutions posted to the website Celsius 2 If your exam grade doesn t match what you remember from the Testing Center it s probably because our website shows you the grade out of 92 not the percentage Kelvin Fahrenheit 3 You can pick up your exams at the usual place 4 The handwritten problems out of 8 pts will hopefully be graded within a couple of days a You will be able to pick them up same place too 5 In case you are curious a 80 of class got velocity vs time graph right up from 66 b 72 of class got work done by normal force up from 62 c 76 of class got cat burglar up from 44 d 74 of class got tension in hanging mass problem up from 46 From warmup Which is coldest a 0 degrees Centigrade Celsius b 0 degrees Kelvin c 0 degrees Fahrenheit What is a thermometer Expansion Thermocouples Resistors Semiconductors Demo two thermometers Just find some property you can measure that changes consistently with temperature Colton Lecture 20 pg 1 Colton Lecture 20 pg 2 What is temperature Thermal expansion Two objects in thermal contact will come to thermal equilibrium they then have the same temperature What is thermal contact able to e h For a given material lengths all change by the same percentage per degree L Lo T A Ao T V Vo T What is heat For solids 2 3 For reference steel 11 10 6 C Is there a maximum temperature You heat up a 1 meter steel rod by 1 degree C How long is it now Is there a minimum temperature Demo bimetallic strip Laser Cooling Atoms slowed by light 2000 Nobel Prize tuned so only atoms moving toward the laser beam can absorb the light momentum they slow down What went wrong here photon photon atom Colton Lecture 20 pg 3 Colton Lecture 20 pg 4 Microscopic View Ideal gases Why do most materials expand when heated 1 Molecules collide like superballs elastic due to repulsive forces 2 No attractive forces 3 Never condense into liquids or solids 4 Are like frictionless surfaces massless pulleys perfect fluids etc Essentially ideal From warmup You heat a disc with a hole in it Will the radius of the hole get larger smaller or stay the same a Larger b Smaller c Stay the same Ideal gas law Demo ball and washer Where does it come from 1 2 Colton Lecture 20 pg 5 Colton Lecture 20 pg 6 Thermodynamics Wish to explain behavior of huge numbers of particles in terms of simple variables Experiments on gases Hold T constant increase P Volume From warmup Ralph is confused the book calls two different equations the ideal gas law In equation 10 8 8th edition the equation is PV nRT But in equation 10 11 8th edition the equation is PV NkBT Why are they both called the ideal gas law when only the first equation looks like what he learned in chemistry Answer from the class Hold P constant increase T Volume Hold P T constant increase N Volume Combine the experimental results PV constant k B NT Boltzmann s constant kB 1 381 10 23 J K PV Nk BT Ideal gas law Physics version Must use T in Kelvin Absolute P From warmup Suppose we have two jars of gas one of helium and one of neon If both jars have the same volume and the two gases are at the same pressure and temperature which jar contains the greatest number of gas molecules Both gases obey the ideal gas law The mass of a neon molecule is greater than the mass of a helium molecule a jar of helium b jar of neon c same number Important N is number of molecules Colton Lecture 20 pg 7 Colton Lecture 20 pg 8 Avagadro s Number and other chemistry concepts Chemists measure quantity in moles NA 1 mole Avagadro s number NA Worked Problem In an engine piston with air at 1 atm the volume is decreased from 200 cm3 to 40 cm3 while the temperature increases from 300 K to 600 K Find the final pressure Method 1 Find N or n N molecules n moles n N NA molar mass mass of one mole careful commonly given in grams n m MM May need to convert to kg Chemistry Ideal Gas Law PV nRT with R NA kB 8 314 J mole K 0 08206 liter atm mole K Method 2 ratios Demo liquid nitrogen and balloons Answer 1 01 106 Pa 10 atm Colton Lecture 20 pg 9 An old fashioned glass milk jug is empty still has air at 20 C You seal it then put it into a fire at 500 C Colton Lecture 20 pg 10 Worked Problem What is the mass of all the air in this room The average molar mass of molecules in air is 29 0 g mol Note assuming the jug doesn t burst N and V are constant Clicker quiz Using the ideal gas law what is the final pressure in the jug a 0 1 atm b 1 2 atm c 2 4 atm d 4 10 atm e 10 atm Worked Problem If instead of being totally empty the jug had a mole of water molecules in it about 18 g how much pressure would they exert after being vaporized assuming the jug still doesn t break Demo nitrogen in tube and balloon Colton Lecture 20 pg 11 Worked Problem Use the ideal gas law to determine the density of air at 1 atm and 300K 80 F MMair 29 g mol Answers depends on room size 1 175 kg m3 Colton Lecture 20 pg 12 Hard Worked Problem if time A hot air balloon wants to lift off on an 80 F day The balloon fabric and basket weight 200 kg and there are four 80 kg passengers The balloon is spherical with an 8 m radius How hot do they have to get the air inside the balloon Hint Do not neglect the weight of the hot air inside the balloon Plan a figure out the maximum mass of hot air b then the density of the hot air then c figure out what temperature gives that density Answers 2000 0 kg 0 9325 kg m3 378 K Colton Lecture 20 pg 13