Entropy & the Second Law

The Second Law of Thermodynamics

Entropy measures how spread out or disordered a system's energy is. Whenever heat flows into an object, its entropy goes up — and the second law says the total entropy of an isolated system never decreases, only stays the same or grows. That's why heat always flows from hot to cold on its own, and why engines can never turn all their heat into useful work.

ΔS = Q / T

• ΔS — entropy change (J/K): how much the system's entropy increases
• Q — heat (J): the heat energy flowing into the system
• T — temperature (K): the absolute temperature at which the heat is added

600 joules of heat flows into a large tank of water held at a steady 300 kelvin. How much does the water's entropy increase?

• Q = 600 J
• T = 300 K

1. ΔS = Q / T
2. ΔS = 600 J / 300 K

ΔS = 2 J/K

The same 600 joules of heat now flows into a cooler tank at 200 kelvin instead. What is the entropy change?

• 1200 J/K
• 3 J/K
• 0.33 J/K

Why does heat flow from a hot cup of coffee into the cooler air of the room, and never the other way around?

• Because that direction increases total entropy
• Because that direction decreases total entropy
• Because both directions keep entropy exactly equal