Kinetic Theory and Thermal Expansion PHYSICS 220 Lecture 23 Kinetic Theory and Thermal Expansion Lecture 23 Purdue University, Physics 220

Purdue University, Physics 220 Ideal Gas Lecture 23 Purdue University, Physics 220

Purdue University, Physics 220 Kinetic Theory Helps to explain gas laws by applying Newton’s law’s to the microscopic molecular motions. The relationship between energy and temperature (for monatomic ideal gas) Lecture 23 Purdue University, Physics 220

Purdue University, Physics 220 Kinetic Theory The relationship between energy and temperature (for monatomic ideal gas) L For N molecules, multiply by N Using PV = NkBT Note <KEtr> = ½m<v2> = 3/2m<vx2> Lecture 23 Purdue University, Physics 220

Purdue University, Physics 220 Kinetic Theory Per molecule Internal energy Lecture 23 Purdue University, Physics 220

Purdue University, Physics 220 Example What is the rms speed of a nitrogen N2 molecule in this classroom? v = 510 m/s = 1150 mph! Lecture 23 Purdue University, Physics 220

Purdue University, Physics 220 iClicker Suppose you want the rms (root-mean-square) speed of molecules in a sample of gas to double. By what factor should you increase the temperature of the gas? A) 2 B) C) 4 Lecture 23 Purdue University, Physics 220

Maxwell-Boltzmann Distribution How many molecules have speeds in a certain range? Lecture 23 Purdue University, Physics 220

Purdue University, Physics 220 Diffusion D … Diffusion constant Lecture 23 Purdue University, Physics 220

Purdue University, Physics 220 Thermal Expansion 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) Temp: T Temp: T+T L0 L Lecture 23 Purdue University, Physics 220

Expansion Coefficients Lecture 23 Purdue University, Physics 220

Purdue University, Physics 220 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 = 100 C M, V100 r100 = M / V100 < r0 T = 0 C M, V0 r0 = M / V0 Lecture 23 Purdue University, Physics 220

Differential Expansion 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 Lecture 23 Purdue University, Physics 220

Purdue University, Physics 220 Thermal Expansion Lecture 23 Purdue University, Physics 220

Purdue University, Physics 220 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 won’t fit through the hole any more B) The ball will fit more easily through the hole C) Same as at room temperature The ball gets larger, but so does the hole! Since they have the same expansion rate, everything will stay the same! Lecture 23 Purdue University, Physics 220

Tight Fit Why does the hole get bigger when the plate expands? Imagine a plate made from 9 smaller pieces. Each piece expands. If you remove one piece, it will leave an “expanded hole” Same object at higer T: Plate and hole both get larger Object at temp T Lecture 23 Purdue University, Physics 220

Purdue University, Physics 220 iClicker 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 Example? Lecture 23 Purdue University, Physics 220

Purdue University, Physics 220 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!  (kg m-3) T (C) Lecture 23 Purdue University, Physics 220

Purdue University, Physics 220 Question Not being a great athlete, and having lots of money to spend, Gill Bates decides to keep the lake in his back yard at the exact temperature which will maximize the buoyant force on him when he swims. Which of the following would be the best choice? A) 0 C B) 4 C C) 32 C D) 100 C E) 212 C The answer is 4 C, because water has its greatest density at 4 C. Since bouyant force is equal to the weight of the displaced fluid or density*volume, when the density is the largest, the bouyant force is maximized. FB = rlVg Lecture 23 Purdue University, Physics 220