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Thermal Physics: Physics of Large Numbers

Disorder always increases over time. Thermal Physics: Physics of Large Numbers. - Avogadro’s number: 6 · 10 23 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.

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Thermal Physics: Physics of Large Numbers

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  1. Disorder always increases over time. Thermal Physics: Physics of Large Numbers - Avogadro’s number: 6·1023 molecules are contained in 2 grams of molecular hydrogen (H2). • 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: Ch. 7

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

  3. The 2nd Law and the Direction of Time • The 2nd lawsingles out a direction oftime. 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 4th 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 spontaneously into a TV set.

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

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

  6. Fig. 7.13 Where Does the Energy Go in a Car? Efficiency = 17/70 = 24% Only (5+5)/70 = 14% actually moves the car.

  7. This part can be used for heating (cogeneration) Energy Flow in a Power Plant Efficiency = 1000/2500 = 40% Fig. 7.21

  8. Optimizing Efficiency • 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). • 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.

  9. C C Is Life Compatible with the 2nd Law? • One might wonder whether the 2nd 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5800K, Tout300K would allow (5800-5300)/5800 = 95% conversion.

  10. N = N N Statistical Error The statistical error of N measurements: (with N electrons, N photons, N persons) Buildup of a diffrac-tion pattern from photons (particles of light). The more photons, the better the visibility.

  11. N/N = 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% Relative Error of Polls, Medical Studies The relative statistical error: (often given in %)

  12. Error of Macroscopic Measurements Typically, a macroscopic objectconsists of1024 atoms (Avogadro’s number). With that many atoms, the relative statistical error is reduced to: 1/1024 = 1/1012 = 1 in a trillion.

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