Physics 101: Lecture 22, Pg 1 Physics 101: Lecture 22 Temperature and Ideal Gas Final

Physics 101: Lecture 22, Pg 2 Internal Energy and Temperature l All objects have “internal energy” (measured in Joules) è random motion of molecules »kinetic energy è collisions of molecules gives rise to pressure l Amount of internal energy depends on è temperature »related to average kinetic energy per molecule è how many molecules »mass è “specific heat” »related to how many different ways a molecule can move n translation n rotation n vibration »the more ways it can move, the higher the specific heat 10

Physics 101: Lecture 22, Pg 3 Temperature Scales Water boils Water freezes Farenheit Celcius Kelvin NOTE: K=0 is “absolute zero”, meaning (almost) zero KE/molecule 14

Physics 101: Lecture 22, Pg 4 Temp Scales Question l Two cups of coffee are heated to 100 degrees Fahrenheit. Cup 1 is then heated an additional 20 degrees Centigrade, cup 2 is heated an additional 20 Kelvin. Which cup of coffee is hotter? A) OneB) TwoC) Same 20

Physics 101: Lecture 22, Pg 5 Thermal Expansion l When temperature rises è molecules have more kinetic energy »they are moving faster, on the average è consequently, things tend to expand l amount of expansion depends on… è change in temperature è original length è coefficient of thermal expansion »L 0 +  L = L 0 +  L 0  T »  L =  L 0  T (linear expansion) »  V =  V 0  T (volume expansion) Temp: T Temp: T+  T L0L0 LL 23

Physics 101: Lecture 22, Pg 6 Density Question As you heat a block of aluminum from 0 C to 100 C its density A. Increases B. Decreases C. Stays the same T = 0 C M, V 0  0 = M / V 0 T = 100 C M, V 100  100 = M / V 100 <  0 26

Physics 101: Lecture 22, Pg 7 Example: concrete sidewalk A concrete (  =12x10 -6 /K) sidewalk is 10m long when poured on a cold day (0 o C) How much will the length of the sidewalk increase on a hot day (35 o C)?

Physics 101: Lecture 22, Pg 8 Example: gas tamk l A steel (β=36x10 -6 /K) gas tank has a volume of 75 lit. You fill it up with gasoline (β=950x10 -6 /K) early in the morning when it is cool During the day the temperature increases by 20 o C. How much gas will spill out?

Physics 101: Lecture 22, Pg 9 Differential Expansion ACT A bimetallic strip is made with aluminum  =16x10 -6 /K on the left, and iron  =12x10 -6 /K on the right. At room temperature, the lengths of metal are equal. If you heat the strips up, what will it look like? A BC Aluminum gets longer, forces curve so its on outside 29

Physics 101: Lecture 22, Pg 10 Amazing Water l Water is very unusual in that it has a maximum density at 4 degrees C. That is why ice floats, and we exist! 30

Physics 101: Lecture 22, Pg 11 Tight Fit An aluminum plate has a circular hole cut in it. An aluminum ball (solid sphere) has exactly the same diameter as the hole when both are at room temperature, and hence can just barely be pushed through it. If both the plate and the ball are now heated up to a few hundred degrees Celsius, how will the ball and the hole fit ? A. The ball wont fit through the hole any more B. The ball will fit more easily through the hole C. Same as at room temperature 35

Physics 101: Lecture 22, Pg 12 Why does the hole get bigger when the plate expands ??? Object at temp T Same object at higer T: Plate and hole both get larger Imagine a plate made from 9 smaller pieces. Each piece expands. If you remove one piece, it will leave an “expanded hole” 36

Physics 101: Lecture 22, Pg 13 A glass jar (  = 3x10 -6 K -1 ) has a metal lid (  = 16x10 -6 K -1 ) which is stuck. If you heat them by placing them in hot water, the lid will be A. Easier to open B. Harder to open C. Same Stuck Lid Question 38 Copper lid expands more, making a looser fit, and easier to open!

Physics 101: Lecture 22, Pg 14 Jar Question A cylindrical glass container (  = 28x10 -6 k -1 ) is filled to the brim with water (  = 208x10 -6 k -1 ). If the cup and water are heated 50C what will happen A) Some water overflows B) Same C) Water below rim 41 Gasoline:  = 950x10-6 k-1, Steel:  = 36x10-6 k-1

Physics 101: Lecture 22, Pg 15 Molecular Picture of Gas l Gas is made up of many individual molecules Number density is number of molecules/volume N/V =  /m   is the mass density è m is the mass for one molecule l Number of moles n=N / N A è N A = Avogadro’s number 6.022x10 23 mole -1 43

Physics 101: Lecture 22, Pg 16 Balloon Question 1 l What happens to the pressure of the air inside a hot-air balloon when the air is heated? (Assume V is constant) 1) Increases 2) Same 3) Decreases Balloon is still open to atmospheric pressure, so it stays at 1 atm 30

Physics 101: Lecture 22, Pg 17 Balloon Question 2 l What happens to the buoyant force on the balloon when the air is heated? (Assume V remains constant) 1) Increases 2) Same 3) Decreases F B =  V g  is density of outside air! 32

Physics 101: Lecture 22, Pg 18 Balloon Question 3 l What happens to the number of air molecules inside the balloon when the air is heated? (Assume V remains constant) 1) Increases 2) Same 3) Decreases PV = NkT P and V are constant. If T increases N decreases. 34

Physics 101: Lecture 22, Pg 19 Kinetic Theory: The relationship between energy and temperature (for monatomic ideal gas) L For N molecules, multiply by N Note KE = ½ m v 2 = 3/2 m v x 2 Using PV = NkT 40

Physics 101: Lecture 22, Pg 20 Example l What is the rms speed of a nitrogen N 2 molecule in this classroom? (T=20 o C)

Physics 101: Lecture 22, Pg 21Summary l Temperature measure of average Kinetic Energy of molecules l Thermal Expansion è  L =  L 0  T (linear expansion) è  V =  L 0  T (volume expansion) l Ideal Gas Law PV = n R T è P = pressure in N/m 2 (or Pascals) è V = volume in m 3 è n = # moles è R = 8.31 J/ (K mole) è T = Temperature (K) l Kinetic Theory of Monatomic Ideal Gas è = 3/2 k B T 50