Lecture 8 Notes: Thermodynamics. Physics Prof. Michael Gold September 24, 2007
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1 Lecture 8 Notes: Thermodynamics Physics Prof. Michael Gold September 24, 2007
2 Thermodynamics: Empirical laws describing average properties of bulk matter. All matter is made up of atoms. Atoms are very small (~0.1 nm) and therefore bulk matter contains a very very large number of atoms. Avogadro s number N A =6.02x10 23 September 25, 2007 physics Lecture 8 1
3 Statistical Mechanics Laws of thermodynamics can be understood (in fact rigorously derived) from the average behavior of molecules (atoms). Thermodynamic laws are rigorously obeyed because the typical number of molecules is so huge that typical deviations from average are immeasurably small and the probability of large deviations is infinitesimally small. September 25, 2007 physics Lecture 8 2
4 Temperature A measure of the mean kinetic energy of molecules per degree of freedom. Degree of freedom is the number of ways a molecule can move. Monatomic: f=3 displacement (v x,v y,v z ) Diatomic: f=5 displacement plus 2 rotational modes at moderate temperatures. September 25, 2007 physics Lecture 8 3
5 Heat A form of energy (molecular kinetic energy) that is transferred between materials as a result of differences in temperature through direct ( thermal ) contact. Heat always flows from hot to cold. September 25, 2007 physics Lecture 8 4
6 Entropy A measure of molecular disorder: The arrow of time: disorder of universe always increases with time. Perpetual motion machines are impossible. A thermodynamic limit to the efficiency of engines. September 25, 2007 physics Lecture 8 5
7 How do we know this? September 25, 2007 physics Lecture 8 6
8 Law of definite proportions Whenever a given compound is formed from two elements, the ratio of the combining masses of the elements is observed to be constant. This holds for every compound although the mass ratio is different for each compound. Dalton (1807)-- Atoms of each element have a definite mass. September 25, 2007 physics Lecture 8 7
9 Example 32g O + 12g C = CO 2 carbon dioxide 16g O + 12g C = CO carbon monoxide Ratio of oxygen in 2 compounds is 2:1 September 25, 2007 physics Lecture 8 8
10 Definition of a Mole 1 mole is an Avogadro s number of things (usually molecules). Like 1 dozen. Empirically defined as the number of carbon atoms in 12 g of carbon. September 25, 2007 physics Lecture 8 9
11 Definition of amu This also defines the atomic mass unit (amu). 12 amu is the mass of 1 carbon atom = mass of 1 mole of carbon / Avogadro s number= 12g/Avogadro s number. Obviously a very small number. The 12 comes from the fact that the carbon-12 atom Contains 6 protons + 6 neutrons (+6 electrons of negligible mass). So 1amu is very nearly the mass of a proton or neutron. September 25, 2007 physics Lecture 8 10
12 Examples 1 mole of hydrogen has a mass of 1g. the hydrogen atom has a mass of 1amu. 1 mole of oxygen has a mass of 16g. The oxygen atom has mass of 16 amu. September 25, 2007 physics Lecture 8 11
13 Density Density = Mass/volume Water density = 1g/cm 3 Water is quite dense. We can measure less-dense substances relative to water via Archimedes principle September 25, 2007 physics Lecture 8 12
14 Density of Ice Unusual property that solid state is less dense than liquid state. density = 0.92 g/cm 3 Think about the implications of this fact for life! September 25, 2007 physics Lecture 8 13
15 Archimedes F B W=F B g x (mass of object) = g x (mass of displaced water) W September 25, 2007 physics Lecture 8 14
16 P = F/(area) Pressure September 25, 2007 physics Lecture 8 15
17 States of matter solid, liquid, gas At very low temperatures Super-fluid (zero viscosity fluid, liquid He-4 Super-conductor High temperatures plasma: ionized gas (e.g. inside fluorescent lamps, stars) Very high temperatures: quark-gluon plasma September 25, 2007 physics Lecture 8 16
18 Measuring Temperature Most substances expand when heated September 25, 2007 physics Lecture 8 17
19 Measure of Heat 1 calorie = heat required to increase the temperature of 1g water by 1 degree C Note: food Calorie = 1 kilocalorie September 25, 2007 physics Lecture 8 18
20 Ideal Gases Important experiments with gases leading to the ideal gas law. Ideal means the limit of non-interacting molecules. An excellent approximation for many gases. September 25, 2007 physics Lecture 8 19
21 Ideal Gas Law P is pressure, V is volume n is number of moles of the gas T is the absolute temperature (Kelvin) R is a universal constant 8.31 J/(mole K) September 25, 2007 physics Lecture 8 20
22 Absolute Temperature (Kelvin scale) September 25, 2007 physics Lecture 8 21
23 Microscopic View A measure of the mean kinetic energy of molecules per degree of freedom. September 25, 2007 physics Lecture 8 22
24 Why is there no hydrogen in the atmosphere? At atmospheric temperatures, H atoms move very fast on average, with a significant fraction exceeding the earth s escape velocity. Over time, the H escapes earth s gravity. We can produce H by separating water which requires energy. Therefore, hydrogen is an energy storage device, not a source of energy on earth. September 25, 2007 physics Lecture 8 23
25 Microscopic view of pressure Atomic collisions are perfectly elastic. How can this be? September 25, 2007 physics Lecture 8 24
26 Measuring Avogadro s Number Einstein (1905) explained Brownian motion (1828) -- the random motion of small particles suspended in liquid-- an terms of motion of molecules of which the liquid is composed. R is displacement of particle of radius r in time t September 25, 2007 physics Lecture 8 25
27 Perrin s Experiment (1908) Devised technique to produce small resin spheres of Uniform size of about 10-6 m (micron) Measured N A = 6 x September 25, 2007 physics Lecture 8 26
28 Weighing the Atom Mass of atom = (atomic mass units)/ Avogadro s number September 25, 2007 physics Lecture 8 27
29 Boltzman s Constant k September 25, 2007 physics Lecture 8 28
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