Temperature and KMT

1. Temperature and KMT AP Physics B Chapter 13 Notes

2. Atomic Theory • Back to some chemistry basics; • AMU (u) defined so 12C is exactly 12.0000 amu (u) • 1 u = 1.6605 x 10-27 kg • Brownian motion evidence of molecular motion • Attractive forces between molecules dictate the state of matter

3. Temperature • Temperature is the measure of how hot or cold something is • Thermometers rely on some property of matter that changes with temperature • Most materials expand with increasing temperature

4. Temperature • Several scales are used: • Farenheit • Celsius (centigrade) • Kelvin (absolute zero) T (˚C) = 5/9{T(˚F) -32} or T (˚F) = 9/5T(˚C) +32 T (K) = T (˚C) + 273.15 • ˚F and ˚C arbitrarily assign temperatures to freezing and boiling points of water

5. Linear Thermal Expansion • Most objects expand when heated—how much varies by material (see Table 13-1 pg. 358) Linear expansion occurs when an object is heated The amount depends on α, the coefficient of linear expansion (units ˚C-1) ∆L = αL0∆T or L = L0(1 + α∆T)

6. Thermal Expansion--Example Ex. 13-3 pg. 358 The steel bed of a suspension bridge is 200m long at 20˚C. If temperature extremes are -30˚C to +40˚C, how much will it contract and expand?

7. Volume Thermal Expansion • Volume expands in a similar fashion with increase in T (affects solids and fluids) ∆V = βV0∆T where β is the coefficient of volume expansion

8. Whacky Water • Water behaves as expected above 4˚C • Below 4˚C water expands as it cools!

9. Gas Laws • Gas laws describe the relationship between volume, pressure, temperature and the mass of the gas • These are known a equations of state • We will look at equilibrium states

10. Gas Laws For a constant mass: • Boyle’s Law: V ∝ 1/P (T constant) • Charles’s Law: V ∝ T (P constant)—at absolute zero, V = 0 • Gay-Lussac’s Law: P ∝ T (V constant)

11. Ideal Gas Law All three previous laws can be combined into one: PV ∝ T But what if mass is not constant? Volume is proportional to mass… PV ∝ mT

12. Ideal Gas Law • To have universal proportionality constant, we need to use number of moles • One mole (mol) is number of grams of a substance that equals its molecular mass

13. Ideal Gas Law • We can now write the ideal gas law: PV = n RT Where R is the universal gas constant Notes: Use T in K; P is absolute http://itl.chem.ufl.edu/2045/MH_sims/gas_sim.html

14. Ideal Gas Law--Example Prob. 35 pg. 381 What is the pressure inside a 35.0L container holding 105kg of argon gas at 385K?

15. Ideal Gas Law--Molecules • Avagadro determined that equal volumes of gas at same T and P contain equal number of molecules (NA = 6.02 x 1023) • We can rewrite the ideal gas law: PV = nRT = N/ NART, where N = # molecules or PV = NkT where k= Boltzmann’s constant k = R/ NA = 1.38 x 10-23 J/K

16. Ideal Gas Law--Example Ex. 13-15 pg. 367 Estimate how many molecules you breathe in a with a 1.0L breath of air.

17. KMT and Temperature • Assumptions of Kinetic Molecular Theory: • Large number of molecules moving in random directions with a variety of speeds • Molecules are far apart on average • Obey Newton’s laws and interact only in collisions • Collisions are elastic http://www.preparatorychemistry.com/KMT_flash.htm

18. KMT and Temperature • Each molecule collides with the wall: • Total force of all molecules: Notes: Use average velocity for 1-D

19. KMT and Temperature • The average of the square of speed in all three directions is the same: • Pressure is P=F/A, so:

20. KMT and Temperature • Rewriting: • Recall PV = NkT so: • Since KE = 1/2mv2 KE = 3/2kT The average kinetic energy of molecules in an ideal gas is directly proportional to temperature of the gas

21. KMT and Temperature • We can solve for v to find how fast molecules are moving on average by taking the root mean square: RMS is the square root of the arithmetic mean of the squares of the original values

22. KMT and Temperature--Example P 51 pg. 381: The rms speed of molecules in a gas at 20˚C is to be increase by 1%. To what temperature must it be raised? P 52 pg. 381: If pressure of a gas is doubled while its volume is held constant, by what factor does vrms change?