Physics 101: Lecture 22 Temperature and Ideal Gas

Final Physics 101: Lecture 22 Temperature and Ideal Gas

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

Temperature Scales Celcius Farenheit Kelvin 373.15 100 212 Water boils 273.15 0 32 Water freezes NOTE: K=0 is “absolute zero”, meaning (almost) zero KE/molecule 14

Temp Scales Question • 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) One B) Two C) Same 20

Thermal Expansion Temp: T L0 Temp: T+T L • When temperature rises • molecules have more kinetic energy • they are moving faster, on the average • consequently, things tend to expand • amount of expansion depends on… • change in temperature • original length • coefficient of thermal expansion • L0 + L = L0 +  L0 T • L =  L0 T (linear expansion) • V =  V0 T (volume expansion) 23

T = 100 C T = 0 C M, V0 r0 = M / V0 M, V100 r100 = M / V100 < r0 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 26

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

Example: gas tamk • 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 20o C. How much gas will spill out?

Differential Expansion ACT • A bimetallic strip is made with aluminum a=16x10-6 /K on the left, and iron a=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 B C Aluminum gets longer, forces curve so its on outside 29

Amazing Water • Water is very unusual in that it has a maximum density at 4 degrees C. That is why ice floats, and we exist! 30

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

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” Why does the hole get bigger when the plate expands ??? 36

Stuck Lid Question A glass jar (a = 3x10-6 K-1) has a metal lid (a = 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 Copper lid expands more, making a looser fit, and easier to open! 38

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

Molecular Picture of Gas • Gas is made up of many individual molecules • Number density is number of molecules/volume N/V = r/m • r is the mass density • m is the mass for one molecule • Number of moles n=N / NA • NA = Avogadro’s number 6.022x1023 mole-1 43

Balloon Question 1 • 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

Balloon Question 2 • What happens to the buoyant force on the balloon when the air is heated? (Assume V remains constant) 1) Increases 2) Same 3) Decreases FB = r V g r is density of outside air! 32

Balloon Question 3 • 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

Kinetic Theory: The relationship between energy and temperature(for monatomic ideal gas) L For N molecules, multiply by N Using PV = NkT Note KE = ½ m v2 = 3/2 m vx2 40

Example • What is the rms speed of a nitrogen N2 molecule in this classroom? (T=20o C)

Summary • Temperature measure of average Kinetic Energy of molecules • Thermal Expansion • L =  L0 T (linear expansion) • V =  L0 T (volume expansion) • Ideal Gas Law PV = n R T • P = pressure in N/m2 (or Pascals) • V = volume in m3 • n = # moles • R = 8.31 J/ (K mole) • T = Temperature (K) • Kinetic Theory of Monatomic Ideal Gas • <Ktr> = 3/2 kB T 50

Physics 101: Lecture 22 Temperature and Ideal Gas