Entropy and the Second Law
Entropy is a state function defined for a reversible differential transfer by dS = δQ_rev/T; for any process, ΔS_universe = ΔS_system + ΔS_surroundings is nonnegative, with equality only for a reversible process.
Why this shows up in the exam
Heating water through a temperature interval · Mixing or free expansion · Testing reversibility and spontaneous direction
Learn the idea
Entropy tracks energy dispersal and determines the allowed direction of spontaneous change. Natural processes can conserve energy yet still be one-way because the total entropy of an isolated system cannot decrease.
🧠 Memory hook: Energy balances quantity; entropy judges direction.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- dS = δQ_rev/T — definition along a reversible path with absolute temperature
- ΔS_universe >= 0 — Clausius statement of the second law; equality denotes reversibility
- ΔS = nC ln(T_f/T_i) — entropy change for heating with constant heat capacity C along a suitable reversible comparison path
How to approach it
- 1Choose a reversible comparison path for the state change
- 2Use kelvin temperatures
- 3Include surroundings before applying the nondecrease rule
Common slip-ups that cost marks
- •Using actual irreversible heat directly in dS = δQ/T
- •Using Celsius in logarithms or denominators
- •Assuming system entropy alone can never decrease
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A gas absorbs 500 J of heat and does 200 J of work. What is the change in its internal energy?
More from Thermodynamics
Thermodynamic Processes and P-V Diagrams
Study different thermodynamic processes (isothermal, isobaric, isochoric, adiabatic, polytropic, cyclic), their definitions, characteristics, and graphical representation on P-V diagrams.
Laws of Thermodynamics
Understand the zeroth and first laws of thermodynamics, including their statements, implications, and applications to physical systems.
Internal Energy, Heat, and Work
Explore the concepts of internal energy, heat, and work, including their definitions, relationships, and how they change during various thermodynamic processes.
Ideal Gas Law and Equation
Learn the ideal gas equation, its relation to physical quantities like pressure, volume, temperature, and density, and its use in describing the behavior of ideal gases.
Gibbs Free Energy and Spontaneity
Learn how Gibbs free energy determines spontaneity, how to calculate it, and its dependence on temperature, pressure, and other thermodynamic parameters.
Entropy and Its Changes
Understand entropy as a measure of disorder, how it changes in physical and chemical processes, and its calculation in various scenarios including phase transitions and isothermal processes.