Thermodynamics – Temperature, Zeroth Law & Thermal Expansion

Overview of Thermodynamics

• Thermodynamics = study of energy flow in the universe as it relates to work, heat, entropy, and other energy forms.
  • Classical (macroscopic) thermodynamics: only observable/ measurable variables (temperature, pressure, volume, work).
  • Statistical model of entropy (microscopic, probabilistic) briefly mentioned to clarify “disorder” concept, but MCAT focuses on macroscopic definition.
• Chapter map
  • Review of Zeroth, First, Second Laws (Third Law only briefly).
  • Zeroth Law → temperature scales.
  • Thermal expansion illustrates relation between thermal energy and physical properties (length, volume, conductivity).
  • Thermodynamic terminology/functions intersect with Ch. 7 of MCAT General Chemistry Review.
  • First Law (conservation of energy): relationship among internal energy, heat, work; specific heat; heat of transformation.
  • Processes moving a system from one equilibrium state to another; link heat with work (ties to Ch. 2 of MCAT Physics & Math Review).
  • Second Law: entropy & its measurement.

Laws of Thermodynamics (Exam-Relevant Emphasis)

• Zeroth Law
  • Observation: If A is in thermal equilibrium with B, and B with C, then A is in thermal equilibrium with C.
  • Consequence: When brought into thermal contact, no net heat flows between objects already in equilibrium.
  • “Thermal contact” can occur without physical contact (across space).
• First Law (preview; detailed later in book)
  • Energy conservation: change in internal energy = heat added − work done by system.
• Second Law (preview)
  • Entropy and directionality of heat flow.
• Third Law (mentioned only)
  • Entropy of a perfectly organized crystal at absolute zero is $0$.

Temperature & Heat

• Temperature
  • Everyday sense = “hot/cold”; precise thermodynamic sense = proportional to average kinetic energy of particles.
  • Temperature difference determines direction of spontaneous heat flow.
• Heat
  • Transfer of thermal energy from higher-T object to lower-T object.
  • If no net heat flows → equal temperatures → thermal equilibrium.

Temperature Scales

• Three common scales: Fahrenheit (°F), Celsius (°C), Kelvin (K).
  • Fahrenheit & Celsius devised using water phase changes (freezing/boiling), convenient for everyday use.
  • Kelvin = SI base unit; zero point is absolute zero (no thermal energy); water freezes at $273.15\text{ K}$.
  • No negative temperatures on Kelvin scale.
• Unit sizes
  • $1\,\text{°C} = 1\text{ K}$ (same magnitude).
  • Fahrenheit degree is smaller (180° between phase changes vs. 100 on °C/K).
• Conversion formulas
  • $F = \frac{9}{5} C + 32$
  • $K = C + 273$
• Example conversion
  • High of $86\,\text{°F}$ →
  • $C = \frac{5}{9}(F-32) = \frac{5}{9}(86-32) = 30\,\text{°C}$
  • $K = 30 + 273 = 303\,\text{K}$

Thermal Expansion

• General observation: physical properties (length, volume, solubility, conductivity) vary with temperature.
  • Historical role in thermometer design (Fahrenheit mercury thermometer): mercury height correlated with reference temperatures (ice–salt bath, ice–water, body temperature).
• Linear Expansion (solids)
  • Rising T → length increases; falling T → length decreases.
  • Equation: $\Delta L = \alpha L \Delta T$
  • $\Delta L$ = change in length.
  • $\alpha$ (alpha) = coefficient of linear expansion (units $\text{K}^{-1}$ or $\text{°C}^{-1}$).
  • $L$ = original length.
  • $\Delta T$ = change in temperature.
• Example (linear expansion)
  • Metal rod: $L=2\,\text{m}$, $\alpha = 1.0 \times 10^{-6}\,\text{K}^{-1}$.
  • Cooled: $T<em>i = 1080\,°C$ → $T</em>f = 80\,°C$.
  • $\Delta L = \alpha L \Delta T = (1.0\times10^{-6})(2)(80-1080)$
  • $\Delta L = -2\times10^{-3}\,\text{m}$ (length decreases).
  • Final length $= 2.000\,\text{m} - 0.002\,\text{m} = 1.998\,\text{m}$.
• Volumetric Expansion (liquids & solids)
  • Equation: $\Delta V = \beta V \Delta T$
  • $\beta$ = coefficient of volumetric expansion.
  • $\beta = 3\alpha$ for isotropic solids.
• Example (volumetric expansion)
  • Mercury thermometer, $V=1\,\text{mL}$.
  • $T<em>i=-25\,°C$, $T</em>f=275\,°C$ ⇒ $\Delta T = 300\,°C$.
  • $\beta = 1.8\times10^{-4}\,\text{K}^{-1}$.
  • $\Delta V = (1.8\times10^{-4})(1)(300) = 5.40\times10^{-2}\,\text{mL} = 0.054\,\text{mL}$.

Conceptual & Real-World Connections

• Thermometers: rely on predictable thermal expansion; calibration grounded in Zeroth Law (equilibrium between thermometer & object).
• Engineering implications
  • Construction joints, bridges, piping require allowances for $\Delta L$ and $\Delta V$ to prevent structural failure.
• Cross-disciplinary links
  • Coefficient of expansion appears in materials science, civil engineering, geophysics (thermal stress in rocks), electronics (thermal management).
• Ethical / practical relevance
  • Accurate temperature measurement critical in medicine, climate science, and industrial safety.
  • Misunderstanding unit conversion (°F ↔ °C) can cause dosing or operational errors.

Key Equations Cheat-Sheet

• Temperature conversions
  • $F = \frac{9}{5}C + 32$
  • $K = C + 273$
• Linear expansion
  • $\Delta L = \alpha L \Delta T$
• Volumetric expansion
  • $\Delta V = \beta V \Delta T$ with $\beta = 3\alpha$.
• Third Law statement (entropy reference)
  • $S_{\text{crystal}}(0\,\text{K}) = 0$