Thermodynamics Laws

Why This Matters

Thermodynamics is the backbone of chemistry—it tells you why reactions happen, whether they'll happen spontaneously, and how much energy is involved. You're being tested on your ability to connect energy flow, entropy changes, and spontaneity into a coherent picture. The AP exam loves asking you to predict reaction direction, calculate enthalpy changes, and explain why certain processes are favorable while others aren't.

Don't just memorize equations and definitions. Every concept here illustrates a deeper principle: energy conservation, entropy increase, temperature-energy relationships, or spontaneity criteria. When you see a thermodynamics question, ask yourself which principle is being tested. Know what each law and equation actually means for chemical systems, and you'll handle anything the exam throws at you.

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The Fundamental Laws: Rules Energy Must Follow

These four laws establish the ground rules for all energy transformations. They're not just abstract principles—they're the framework you'll use to analyze every thermodynamic problem.

Zeroth Law of Thermodynamics (Thermal Equilibrium)

• Establishes the concept of temperature—if system A is in thermal equilibrium with system C, and system B is also in equilibrium with C, then A and B are in equilibrium with each other
• Allows temperature measurement by defining what it means for objects to be "at the same temperature"
• Underpins heat transfer analysis—without this law, we couldn't meaningfully compare temperatures between systems

First Law of Thermodynamics (Conservation of Energy)

• Energy is conserved—it cannot be created or destroyed, only converted between forms
• Mathematical form: $\Delta U = q + w$ where $\Delta U$ is internal energy change, $q$ is heat, and $w$ is work done on the system
• Tracks energy accounting in all processes—every joule must be accounted for in chemical reactions, phase changes, and physical processes

Second Law of Thermodynamics (Entropy)

• Entropy of the universe always increases for spontaneous processes—systems naturally move toward greater disorder
• Explains directionality—why heat flows from hot to cold, why gases expand, why reactions proceed in one direction
• Limits efficiency of all real processes—you can never convert heat entirely into work

Third Law of Thermodynamics (Absolute Zero)

• Entropy approaches zero as temperature approaches $0 \text{ K}$ for a perfect crystal
• Absolute zero is unattainable—you cannot reach $0 \text{ K}$ in a finite number of steps
• Provides reference point for calculating absolute entropy values, which appear in standard entropy tables

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Gas Behavior: Pressure, Volume, and Temperature Relationships

Gas laws describe how macroscopic properties relate to each other. These relationships emerge from the kinetic molecular theory—gas particles in constant motion, colliding with walls and each other.

Ideal Gas Law

• $PV = nRT$ combines all gas variables into one equation, where $R = 8.314 \text{ J/(mol·K)}$ or $0.0821 \text{ L·atm/(mol·K)}$
• Assumes ideal conditions—no intermolecular forces, negligible particle volume; best at high temperature and low pressure
• Foundation for stoichiometry involving gases—use it to convert between moles and volume at any conditions

Boyle's Law

• Pressure and volume are inversely proportional at constant temperature: $P_1V_1 = P_2V_2$
• Explains compression and expansion—squeeze a gas into smaller volume, pressure increases proportionally
• Isothermal processes follow this relationship; appears in PV diagrams as hyperbolic curves

Charles's Law

• Volume and temperature are directly proportional at constant pressure: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$
• Temperature must be in Kelvin—this is non-negotiable; using Celsius will give wrong answers
• Explains thermal expansion of gases and why hot air balloons rise

Gay-Lussac's Law

• Pressure and temperature are directly proportional at constant volume: $\frac{P_1}{T_1} = \frac{P_2}{T_2}$
• Applies to rigid containers—aerosol cans, car tires, any system where volume can't change
• Explains pressure increases when gases are heated in closed containers

Combined Gas Law

• Merges Boyle's, Charles's, and Gay-Lussac's laws: $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$
• Use when multiple variables change—more versatile than individual laws for real problems
• Reduces to simpler laws when one variable is held constant; good for checking your work

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Energy Transfer: Heat, Work, and Capacity

These concepts quantify how energy moves between systems and surroundings. Understanding the mechanisms of energy transfer is essential for thermodynamic calculations.

Heat Capacity and Specific Heat

• Heat capacity ($C$) is the total heat needed to raise a system's temperature by $1°\text{C}$; specific heat ($c$) is heat capacity per gram
• Equation: $q = mc\Delta T$ where $m$ is mass and $\Delta T$ is temperature change
• Water's high specific heat ($4.18 \text{ J/(g·°C)}$) is a frequent exam topic—explains climate moderation and biological temperature regulation

Latent Heat and Phase Changes

• Heat absorbed/released without temperature change during phase transitions—all energy goes into breaking or forming intermolecular forces
• $q = m \Delta H_{fus}$ for melting/freezing; $q = m \Delta H_{vap}$ for boiling/condensation
• Heating curves show plateaus at phase changes where temperature stays constant despite heat input

Work in Thermodynamic Systems

• Pressure-volume work: $w = -P\Delta V$ for expansion/compression against constant external pressure
• Negative sign convention—work done by the system (expansion) is negative; work done on the system (compression) is positive
• Appears in First Law calculations—you must account for both $q$ and $w$ to find $\Delta U$

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Thermodynamic State Functions: Predicting Reactions

State functions depend only on current conditions, not on how the system got there. These quantities let you predict reaction behavior without knowing mechanistic details.

Enthalpy

• $H = U + PV$ represents total heat content; $\Delta H$ measures heat flow at constant pressure
• Negative $\Delta H$ = exothermic (releases heat); positive $\Delta H$ = endothermic (absorbs heat)
• Hess's Law lets you calculate $\Delta H$ by summing enthalpy changes of intermediate steps—state function property in action

Gibbs Free Energy

• $\Delta G = \Delta H - T\Delta S$ combines enthalpy and entropy to predict spontaneity
• Negative $\Delta G$ = spontaneous; positive $\Delta G$ = non-spontaneous; $\Delta G = 0$ = equilibrium
• Temperature dependence is key—reactions with $+\Delta H$ and $+\Delta S$ become spontaneous at high $T$; those with $-\Delta H$ and $-\Delta S$ become spontaneous at low $T$

Carnot Cycle and Heat Engines

• Maximum theoretical efficiency: $\eta = 1 - \frac{T_{cold}}{T_{hot}}$ where temperatures are in Kelvin
• Four reversible processes—two isothermal (constant $T$) and two adiabatic (no heat exchange)
• Real engines are always less efficient than Carnot efficiency—Second Law guarantee

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Quick Reference Table

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Self-Check Questions

1. Which two gas laws would you combine to analyze a process where both temperature and volume change while the amount of gas stays constant?

2. A reaction has $\Delta H = +50 \text{ kJ/mol}$ and $\Delta S = +150 \text{ J/(mol·K)}$. At what temperature does this reaction become spontaneous? Which thermodynamic quantity determines this?

3. Compare and contrast specific heat and latent heat: when do you use each in a heating curve calculation, and why does temperature behave differently in each region?

4. How does the Second Law of Thermodynamics explain why the Carnot efficiency formula sets a maximum—not typical—efficiency for heat engines?

5. An FRQ asks you to determine whether a reaction is spontaneous at 298 K given $\Delta H$ and $\Delta S$ values. What equation do you use, and what sign of your answer indicates spontaneity?