Thermodynamics Study Guide

📖 Core Concepts Thermodynamics – study of heat, work, temperature, and their link to energy & entropy. State function – property (e.g., U, H, G) that depends only on the current state, not on how the system got there. System vs. surroundings – the defined region of interest; everything outside is the surroundings. Intensive vs. extensive variables – intensive (T, p) independent of size; extensive (V, U, m) scale with amount of material. Thermodynamic potentials – energies (U, H, A, G) that are minimized under specific constraints, predicting equilibrium & spontaneity. Conjugate variable pairs – force–displacement pairs that quantify work: \(p\)–\(V\) (mechanical), \(T\)–\(S\) (thermal), \(\mu\)–\(N\) (chemical). 📌 Must Remember Zeroth Law – Thermal equilibrium is transitive; defines temperature. First Law: \(\Delta U = Q - W\). Energy is conserved; \(\Delta U\) is a state function. Second Law – Entropy of an isolated system never decreases; heat flows spontaneously from hot → cold. Third Law – Entropy of a perfect crystal → constant (often taken as 0) as \(T \rightarrow 0\) K. System types: Isolated – no heat, work, or matter exchange. Closed – heat & work exchange, no matter. Open – heat, work, and matter exchange. Common processes: Adiabatic: \(Q = 0\). Isothermal: \(T = \text{const}\). Isobaric: \(p = \text{const}\). Isochoric: \(V = \text{const}\). Isentropic: \(S = \text{const}\) (reversible adiabatic). Isenthalpic: \(H = \text{const}\). Potentials: \(H = U + pV\) – constant‑\(p\) work. \(A = U - TS\) – constant‑\(T, V\). \(G = H - TS = U + pV - TS\) – constant‑\(T, p\). 🔄 Key Processes Adiabatic (reversible) No heat transfer \((Q=0)\). Use \(\Delta U = -W\) and \(pV^\gamma = \text{const}\) (ideal gas). Isothermal (ideal gas) \(T\) constant → \(\Delta U = 0\). Work: \(W = nRT \ln\frac{V2}{V1}\). Heat added equals work done: \(Q = W\). Isobaric \(p\) constant → \(W = p\Delta V\). Enthalpy change \(\Delta H = Q{p}\) (heat at constant pressure). Isochoric \(V\) constant → \(W = 0\). Heat added changes internal energy: \(\Delta U = Q{V}\). Isentropic (ideal gas) \(S\) constant → \(pV^\gamma = \text{const}\) and \(TV^{\gamma-1}= \text{const}\). 🔍 Key Comparisons Adiabatic vs. Isothermal – Adiabatic: \(Q=0\); temperature may change. Isothermal: \(T\) fixed; heat flows to keep \(ΔU=0\). Isobaric vs. Isochoric – Isobaric: pressure fixed, volume can change → work done. Isochoric: volume fixed, no work. Isentropic vs. Adiabatic – All isentropic processes are adiabatic and reversible; adiabatic can be irreversible (entropy increases). Enthalpy (H) vs. Internal Energy (U) – \(H\) adds the \(pV\) work term; useful when pressure is the controlled variable. ⚠️ Common Misunderstandings “Heat = temperature” – Heat is energy transfer; temperature is an intensive property indicating average kinetic energy. “ΔU = Q” – Only true for processes with no work; generally \(\Delta U = Q - W\). “Isentropic = No entropy change ever” – True only for reversible adiabatic processes; any friction or irreversibility breaks the condition. “Enthalpy is always heat” – Enthalpy change equals heat only at constant pressure. 🧠 Mental Models / Intuition Energy bookkeeping – Treat the system like a bank account: heat in (+), work out (–), and the balance is the change in internal energy. Potential “downhill” – A thermodynamic potential (U, H, A, G) acts like gravitational potential energy; the system spontaneously moves toward lower potential under its constraints. Conjugate pairs as “force × distance” – Just as force × displacement gives mechanical work, \(p·ΔV\) and \(T·ΔS\) give pressure‑volume and thermal work. 🚩 Exceptions & Edge Cases Phase changes – Entropy and volume can jump discontinuously; the usual \(pV^\gamma\) relations do not apply. Non‑ideal gases – Ideal‑gas equations (e.g., \(pV=nRT\)) fail at high pressure/low temperature; use real‑gas equations of state. Open systems – Energy balance must include enthalpy flow of matter: \(\Delta U = Q - W + \sum \dot{m}i hi\). 📍 When to Use Which Constant pressure → work with enthalpy (H); heat at constant \(p\) equals \(\Delta H\). Constant temperature & volume → use Helmholtz free energy (A); spontaneous change if \(\Delta A < 0\). Constant temperature & pressure → use Gibbs free energy (G); most common for chemical reactions. Closed, no heat exchange → apply first‑law adiabatic relation \(\Delta U = -W\). Open, steady‑state flow → employ control‑volume energy balance with enthalpy terms. 👀 Patterns to Recognize “ΔS > 0 for isolated system” → process is spontaneous (Second Law). “Constant‑p, constant‑T” → look for Gibbs free energy. “No heat term in first law” → process is adiabatic. “Zero work term (ΔV = 0)” → process is isochoric; internal energy change equals heat added. 🗂️ Exam Traps Choosing the wrong potential – Selecting \(A\) when the problem fixes pressure (instead of volume) leads to incorrect spontaneity criterion. Confusing \(Q\) and \(ΔU\) – Some questions state “heat added” but expect you to account for work; remember \(\Delta U = Q - W\). Assuming all adiabatic processes are reversible – Irreversible adiabatic processes increase entropy; only isentropic processes are reversible adiabatic. Mixing up intensive vs. extensive – Treating pressure as additive with system size is wrong; pressure is intensive. Neglecting sign convention for work – By convention, work done by the system is positive in many textbooks, but the outline uses \(ΔU = Q - W\) (work done by the system positive). Ensure you follow the given sign convention.