Heat, Entropy, and the Arrow of Time
Key ideas from thermodynamics: heat as molecular motion, entropy as counting microstates, and the limits on engines.
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Questions Covered in This Set
10 cards to master
Temperature (physical definition)
A measure of the average kinetic energy per molecule in a substance.
Heat
Energy transferred from one system to another because of a temperature difference.
First Law of Thermodynamics (equation and meaning)
ΔU = Q − W: the change in internal energy equals heat added minus work done by the system. It is energy conservation, and says nothing about direction.
Macrostate vs. microstate
A macrostate is what you can measure (temperature, pressure, volume); a microstate is the exact position and velocity of every particle. Many microstates give the same macrostate.
Boltzmann's entropy formula
S = k_B ln W, where W is the number of microstates consistent with the macrostate and k_B is Boltzmann's constant.
Second Law of Thermodynamics
The entropy of an isolated system never decreases — systems wander from rare configurations into overwhelmingly more common ones.
Why does the four-coin example matter?
There is 1 way to get all heads but 6 ways to get two heads and two tails, so 'two and two' shows up more often — entropy is just counting, not a force.
Carnot's maximum efficiency
η_max = 1 − T_C/T_H, with temperatures in kelvin; no heat engine between those reservoirs can do better.
Carnot limit for steam at 800 K exhausting to a 300 K river
1 − 300/800 = 62.5% maximum; real plants reach about 40% after friction and losses.
Why can't you unscramble an egg if energy is conserved?
Energy conservation allows it, but the ordered state corresponds to vastly fewer microstates — statistics, not energy, forbids the reverse.
