Lecture 21 Announcements 1 Exam solutions posted to the website 2 You can pick up your exams at the usual place 3 The handwritten problems out of 8 pts will hopefully be graded within the next day or two a You will be able to pick them up same place too From last time Worked Problem A flat roof of area 400 m2 will rip off if it is subjected to a lift force of 5 105 N What speed of horizontal wind will rip off the roof weight of the roof is included in 5 105 N number air 1 29 kg m3 Answer 44 0 m s Clicker quiz A ball is thrown toward you spinning so that the left side of the ball as you look at it spins toward you and the right side away The ball will a float more than a nonspinning ball b sink faster than a nonspinning ball c curve to your left d curve to your right Colton Lecture 21 11 11 08 pg 1 Colton Lecture 21 11 11 08 pg 2 What is temperature Temperature scales Demo flaming jar Celsius Centigrade Two objects in thermal contact will come to thermal equilibrium they then have the same temperature Kelvin What is thermal contact able to What is heat Fahrenheit Is there a maximum temperature What is a thermometer Is there a minimum temperature Expansion Thermocouples Demo two thermometers Laser Cooling Atoms slowed by light 2000 Nobel Prize only atoms moving toward the laser beam can absorb the light momentum they slow down Resistors Semiconductors photon photon Just find some property you can measure that changes consistently with temperature Colton Lecture 21 11 11 08 pg 3 atom Colton Lecture 21 11 11 08 pg 4 Thermal expansion For a given material lengths all change by the same percentage per degree Microscopic View Why do most materials expand when heated L Lo T A Ao T V Vo T For solids 2 3 For reference steel 11 10 6 C You heat up a 1 meter steel rod by 1 degree C How long is it now Demo bimetallic strip Clicker quiz 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 Ralph question What went wrong here Demo ball and washer Colton Lecture 21 11 11 08 pg 5 Colton Lecture 21 11 11 08 pg 6 Thermodynamics Ideal gases 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 Wish to explain behavior of huge numbers of particles in terms of simple variables Experiments on gases Hold T constant increase P Volume Hold P constant increase T Volume Hold P T constant increase N Volume Ideal gas law Combine the experimental results PV constant k B NT Where does it come from Boltzmann s constant kB 1 381 10 23 J K PV Nk BT Ideal gas law Physics version N is number of molecules Colton Lecture 21 11 11 08 pg 7 Colton Lecture 21 11 11 08 pg 8 Must use T in Kelvin Absolute P Avagadro s Number and other Chemistry concepts Molecular view Chemists measure quantity in moles NA 1 mole Avagadro s number NA N molecules n moles n N NA molar mass mass of one mole careful commonly given in grams n m MM Specifically each degree of freedom of each molecule has thermal energy of May need to convert Chemistry Ideal Gas Law PV nRT with R NA kB Equipartition Theorem and speed of molecules The total kinetic energy of a system is shared equally among all of its independent parts on the average once the system has reached thermal equilibrium 8 314 J mole K 0 08206 liter atm mole K Demo liquid nitrogen and balloons Colton Lecture 21 11 11 08 pg 9 independent parts larger for molecules that can rotate vibrate requires more than one atom such molecules have more internal energy Average rms kinetic energy of a molecule Result vrms 3k BT m 3 RT MM Colton Lecture 21 11 11 08 pg 10 Molecular View of Pressure An ideal gas has a mixture of heavy and light molecules Pressure due to collision forces from molecules Clicker quiz 1 The molecules that move the fastest are a heavy b light c same Force per molecule averaged over time F ma m v t what should t be v is proportional to vrms t is proportional to 1 vrms Then the force and hence pressure is proportional to Clicker quiz 2 warmup The molecules with the most KE are a heavy b light c same Clicker quiz 3 If you have equal numbers of heavy and light molecules in the gas the ones that exert the most pressure on average are a heavy b light c same Hint think of the ideal gas law ideal gas law Demo collisions and pressure Colton Lecture 21 11 11 08 pg 11 Colton Lecture 21 11 11 08 pg 12 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 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 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 Method 2 ratios Demo nitrogen in tube and balloon Answer 1 01 106 Pa 10 atm Colton Lecture 21 11 11 08 pg 13 Worked Problem What is the mass of all the air in this room Colton Lecture 21 11 11 08 pg 15 Colton Lecture 21 11 11 08 pg 14