Imagine your room. Sometimes it's super neat (low entropy) and sometimes, well, let's call it creative chaos (high entropy). Entropy measures this chaos or disorder in systems, like our universe!

• Entropy (S) = Measure of disorder.
• Microstates: Different arrangements of molecules.
  • E.g., Molecules in gas have lots of positions and speeds.
• Formula: S = kB ln Ω
  • Ω: Number of arrangements.
  • kB: Boltzmann constant (thanks to Ludwig Boltzmann!).
• Atoms in solids: Can be in perfect order (1 arrangement) or have gaps (many arrangements = increased entropy).

• A perfect copper crystal lattice.
• Remove one atom. Now there are many ways this lattice can be, and thus, more entropy!

• Dice Game
  • Box with 6 counters (1 to 6) & an empty box.
  • Roll a dice and move the counter with that number to the empty box.
  • On average, you'll have 3 counters in each box after playing for a long time.
• Maths Behind
  • 2 possibilities for each counter, hence for 6 counters, it's 2⁶ = 64 arrangements (microstates).
  • 3 counters in each box is one of the macrostates, but there are many microstates to achieve this.

• Represents expansion of a gas into a larger volume.
• More space = more possible arrangements for gas molecules.
• Formula: ΔS = kBN ΔV/V

• Gas expanding does work (PΔV).
• Q = T × ΔS or ΔS = Q/T
  • Where Q is energy transfer at a given temperature T.