Which formula links entropy S to multiplicity W?
- S equals W over k
- S equals k times W
- S equals k ln W
What is a microstate?
- One exact microscopic arrangement
- The measured pressure
- The average energy
The second law forbids entropy decrease the way energy conservation forbids free work.
Circle one: True False
Why does entropy use the logarithm of multiplicity?
- To keep entropy additive when systems combine
- Because logs look nicer
- To hide the units
Toss four coins and count heads versus tails. Which outcome owns the most microstates?
- All heads
- Two heads and two tails
- All tails
Could all the air molecules in a room gather in one corner on their own?
- Forbidden absolutely
- Happens about every hour
- Possible but astronomically unlikely
Two independent systems combine and the total multiplicity squares. What happens to the entropy?
- It doubles
- It squares
- It halves
Modern experiments watch just a handful of particles. What do they see?
- No motion at all
- Entropy flickering down briefly, as fluctuation theorems quantify
- The second law failing permanently
Counting arrangements: multiplicity and entropy W1-mt_55I3VvYMc6-s1
- S equals k ln W · Boltzmann's formula is S equals k times the natural log of W.
- One exact microscopic arrangement · A microstate pins every molecule to a position with a velocity.
- False · Decreases are fantastically improbable, not forbidden.
- To keep entropy additive when systems combine · Multiplicities multiply while logs add, so doubled systems double entropy.
- Two heads and two tails · The 2-2 split owns six sequences, beating one each for the extremes.
- Possible but astronomically unlikely · Nothing bans it, but its pile of microstates is vanishingly tiny.
- It doubles · Log of a square is twice the log, so entropy doubles.
- Entropy flickering down briefly, as fluctuation theorems quantify · Small counts let entropy dip briefly before the pile reclaims it.