Thermal Physics: Physics of Large Numbers

- Avogadro’s number: 6 · 1023 moleculesare 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

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 2nd law:

see Lect. 4, Slide 5

Entropy always increases over time.

The 2nd Law and the Direction of Time

• The 2nd 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 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.

• 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 EnergyInput 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 2nd law of thermodynamics sets an upper efficiency limit:

T is the absolute temperature in degrees Kelvin.Kelvin = Celsius + 2730

Thermal Efficiency < = 100% Tin Tout

Tin

Tout

Tin

Where Does the Energy Go in a Car ?

Fig. 7.13

Efficiency = 17/70 = 24% Only (5+5)/70 = 14% actually moves the car.

Energy Flow in a Power PlantThis part can be used for heating (cogeneration)

Fig. 7.21

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 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.

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 =

= 0.033 = 3.3 %

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 .

Error of Macroscopic Measurements