Thermal Physics: Physics of Large Numbers -Avogadro’s number: 6 · 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: Ch. 7 Disorder always increases over time.

Entropy Entropy is a quantitative measure of disorder. 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 : see Lect. 4, Slide 5 Entropy always increases over time.

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 spontaneously into a TV set.

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 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. Efficiency Output Energy Input Energy Efficiency =

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: T is the absolute temperature in degrees Kelvin. Kelvin = Celsius Thermal Efficiency < = 100% T in T out T in T out T in

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

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

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.

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. T in  5800 K, T out  300 K would allow ( )/5800 = 95% conversion. C C

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

Relative Error of Polls, Medical Studies The relative statistical error: (often given in %)  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 = = = 3.3 %

Typically, a macroscopic object consists of atoms (Avogadro’s number). With that many atoms, the relative statistical error is reduced to: 1/  = 1/10 12 = 1 in a trillion. Error of Macroscopic Measurements