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:
Disorder always increases over time.
Ch. 7
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 2nd law :
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.
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.
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:
Tin Tout
Thermal Efficiency <
= 100%
Tin
Tout
Tin
T is the absolute temperature in degrees Kelvin.
Kelvin = Celsius + 2730
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 Plant
This part can be used for
heating (cogeneration)
Efficiency =
1000/2500 = 40%
Fig. 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.
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  5800 K, Tout  300 K 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
Buildup of a diffraction pattern from
photons (particles
of light). The more
photons, the better
the visibility.
N
Relative Error of Polls, Medical Studies
The relative statistical error:
(often given in %)
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 %
N/N = N/N = 1/N
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 .