Thermal Physics Physics of Large Numbers Avogadros number

Thermal Physics: Physics of Large Numbers - Avogadro’s number: 6 · 1023 molecules are contained in 2 grams of molecular hydrogen (H 2). – New laws of statistical physics emerge when such large numbers of particles are involved. – The most important of those laws is the second law of thermodynamics. Here is a crude version: Disorder always increases over time. Phy 107 Spr 07, Lecture 7 Ch. 17

Entropy • Entropy is a quantitative measure of disorder. see Lect. 4, Slide 5 • Entropy is defined as the logarithm of the number of microscopic configurations which cannot be distinguished macroscopically (for example the velocities of all the air molecules in a balloon). • That allows a quantitative form of the 2 nd law : Entropy always increases over time. Phy 107 Spr 07, Lecture 7 2

The 2 nd Law and the Direction of Time • The 2 nd law singles out a direction of time. The future becomes different from the past, i. e. more disordered. • The laws of gravity and electromagnetism are symmetric in time. A movie played backwards is still fully compatible with them. • But throwing a TV set from the 4 th floor to the ground is not reversible. Statistical physics comes into play when the TV set disintegrates and converts its kinetic energy into thermal energy of trillions and trillions of atoms. They will never reassemble Phy 107 spontaneously into a TV set. Spr 07, Lecture 7 3

Efficiency • For any kind of energy conversion the efficiency is defined as : Output Energy Efficiency = Input Energy (e. g. for conversion of solar to electric energy by a solar cell) • We distinguished two types of energy, high and low quality. • High quality energy can be converted fully into any other form of energy (kinetic, electric, chemical, thermal, …). • Low quality energy = thermal energy can only be converted partially, since the atoms cannot be forced to move orderly. Phy 107 Spr 07, Lecture 7 4

Maximum Thermal Energy Conversion Efficiency For the conversion of thermal energy into high quality energy (such as electric, chemical, kinetic, and gravitational energy) the 2 nd law of thermodynamics sets an upper efficiency limit: Tin Tout Thermal Efficiency < = 100% Tin Tout Tin T is the absolute temperature in degrees Kelvin = Celsius + 2730 Phy 107 Spr 07, Lecture 7 5

Where Does the Energy Go in a Car ? Fig. 7. 13 Efficiency = 17/70 = 24% Only (5+5)/70 = 14% actually moves the 6 car. Phy 107 Spr 07, Lecture 7

Energy Flow in a Power Plant This part can be used for heating (cogeneration) Efficiency = 1000/2500 = 40% Phy 107 Spr 07, Lecture 7 Fig. 7 7. 21

Optimizing Efficiency 1. Avoid conversion of high quality energy into heat. Examples: Use an electric motor instead of a combustion engine ( 95% vs. 24% efficiency ); Convert fuel directly to electricity by fuel cells; Use regenerative braking, where kinetic energy is converted back to electric energy by running an electric motor in reverse (electric train, car). 2. If that’s not possible, run at high temperature. Examples: Build ceramic car engines which run at high temperature; Run power plants at high temperature; Use diesel-electric locomotives where a diesel generator drives electric motors. Phy 107 Spr 07, Lecture 7 8

Is Life Compatible with the 2 nd Law ? • One might wonder whether the 2 nd law allows the complexity of life , the huge genome, organized cities, sophisticated silicon chips. • Life is only possible because the Sun provides high quality energy for the Earth. Without sunlight we would be dead (no food). • Plants convert only 2% of the light into high quality chemical energy. Tin 5800 K, Tout 300 K would allow (5800 -5300)/5800 = 95% conversion. Phy 107 Spr 07, Lecture 7 C C 9

Statistical Error The statistical error of N measurements: (with N electrons, N photons, N persons) N = N Buildup of a diffraction pattern from photons (particles of light). The more photons, the better the visibility. N Phy 107 Spr 07, Lecture 7 10

Relative Error of Polls, Medical Studies The relative statistical error: (often given in %) N/N = 1/ N Example (N persons): Accuracy of a poll, clip from the Wisconsin State Journal Oct. 4, 2012, p. 1. Here: 1/ N = 1/ 894 = = 0. 033 = 3. 3 % Phy 107 Spr 07, Lecture 7 11

Error of Macroscopic Measurements Typically, a macroscopic object consists of 1024 atoms (Avogadro’s number). With that many atoms, the relative statistical error is reduced to: 1/ 1024 = 1/1012 = 1 in a trillion. Phy 107 Spr 07, Lecture 7 12