First Law of Thermodynamics & Heat: Comprehensive Study Notes

First Law of Thermodynamics

• Statement
  • $\Delta U = Q - W$
  • $\Delta U$: change in internal energy of a system.
  • $Q$: energy transferred into the system as heat.
  • $W$: work done by the system on the surroundings.
  • Originates from universal conservation of energy: energy is neither created nor destroyed, only transformed.
  • Incorporates all forms of work (including friction, air resistance, viscous drag), so non-conservative forces pose no problem.
• Sign conventions
  • $\Delta U$
  • Positive → temperature rises.
  • Negative → temperature falls.
  • $Q$
  • Positive → heat flows into the system.
  • Negative → heat flows out of the system.
  • $W$
  • Positive → work done by the system (expansion).
  • Negative → work done on the system (compression).
• Connection to mechanical-energy conservation (Chapter 2 review)
  • In absence of non-conservative forces, $K + U$ is constant; first law generalises this when heat/work are present.
• Everyday illustration
  • Car “burning rubber”: mechanical energy seemingly lost, but first law tracks it as thermal energy in tires, road, and air.

Heat: Definition, Units, & Thermodynamic Laws

• Zeroth Law recap: objects in thermal contact with identical temperature → thermal equilibrium.
• Second Law corollary: heat flows spontaneously from higher-T body to lower-T body until equilibrium is reached; reverse flow requires external work.
• Heat (process variable)
  • Energy transferred because of temperature difference.
• SI & common units
  • Joule (J).
  • calorie (cal, lower-case).
  • Nutritional Calorie (Cal or kcal): $1\,\text{Cal} = 10^3\,\text{cal}$.
  • British thermal unit (BTU).
  • Conversions: $1\,\text{Cal} = 10^3\,\text{cal} = 4184\,\text{J} = 3.97\,\text{BTU}$.

Mechanisms of Heat Transfer

• General requirement: thermal contact (not necessarily physical contact).
• Conduction
  • Direct molecular collisions transfer energy.
  • Metals → excellent conductors (electron sea).
  • Gases → poor conductors (large intermolecular spacing).
  • Ex: fingertip on hot stove.
• Convection
  • Energy carried by bulk flow of a fluid (liquid or gas).
  • Hot fluid over cooler surface transfers heat.
  • Applications: convection ovens (fan-driven hot air → faster cooking); cold-water baths for rapid cooling in labs.
• Radiation
  • Electromagnetic waves carry energy; no medium required → works through vacuum.
  • Sun heating Earth; radiant electric/gas ovens.

Specific Heat $c$

• Definition: heat needed to raise $1\,\text{g}$ of a substance by $1\,^{\circ}!\text{C}$ (or $1\,\text{K}$).
  • Water (liquid) standard: $c<em>{\text{H}</em>2\text{O}} = 1\,\text{cal}\,\text{g}^{-1}\,\text{K}^{-1} = 4.184\,\text{J}\,\text{g}^{-1}\,\text{K}^{-1}$.
• Temperature-change formula
  • $Q = m c \Delta T$
  • $m$: mass.
  • $\Delta T$: change in °C or K (identical magnitude).
• Phase dependence: $c$ differs for solid, liquid, gas phases of same substance.

Heat of Transformation (Latent Heat)

• During phase change, temperature remains constant even as heat flows.
• Molecular view
  • Added heat changes potential energy (freedom of arrangement/number of microstates), not average kinetic energy.
  • Ice at $0^{\circ}!\text{C}$ vs. water at $0^{\circ}!\text{C}$: same $\bar{K}$, but liquid has higher potential energy and more microstates.
• Equation for phase-change heat
  • $Q = m L$
  • $L$: latent heat / heat of transformation (J kg$^{-1}$).
• Terminology
  • Melting/freezing (solid↔liquid) at melting point → heat of fusion $L_f$.
  • Boiling/condensation (liquid↔gas) at boiling point → heat of vaporization $L_v$.
• Example (worked in transcript)
  • Data
  • Silver: $T<em>m = 962^{\circ}!\text{C}$, $L</em>f \approx 1.05 \times 10^5\,\text{J kg}^{-1}$, $c_{\text{Ag}} = 233\,\text{J kg}^{-1}\,\text{K}^{-1}$.
  • Initial $T_i = 20^{\circ}!\text{C}$, mass $m = 1\,\text{kg}$.
  • Step 1: raise to melting point
    $Q_1 = m c \Delta T = (1)(233)(962 - 20) \approx 2.19 \times 10^5\,\text{J}$ (219 kJ).
  • Step 2: melt
    $Q<em>2 = m L</em>f = (1)(1.05 \times 10^5) = 1.05 \times 10^5\,\text{J}$ (105 kJ).
  • Total heat required
    $Q<em>{\text{tot}} = Q</em>1 + Q_2 \approx 3.24 \times 10^5\,\text{J} = 324\,\text{kJ}$.

Thermodynamic Processes & PV Representation

• A process moves the system from an initial equilibrium state $(P<em>i, V</em>i, T<em>i)$ to a final one $(P</em>f, V<em>f, T</em>f)$.
• Key special processes (MCAT emphasis)
  • Isothermal (constant $T$)
  • $\Delta U = 0$ → first law reduces to $Q = W$.
  • Adiabatic (no heat exchange $Q = 0$)
  • $\Delta U = -W$.
  • Isovolumetric / Isochoric (constant $V$)
  • $W = 0$ → $\Delta U = Q$.
  • Isobaric (constant $P$)
  • Less emphasized; multiple algebraic forms exist.
• PV-graph insights
  • Work done by system = area under $P(V)$ curve.
  • Closed loop path → net work = area enclosed (direction: clockwise = positive work by system).
• Example (constant-pressure expansion)
  • Data: $P = 3.6 \times 10^5\,\text{Pa}$, $Q<em>{\text{in}} = 300\,\text{kJ}$, $V</em>i = 1.0\,\text{m}^3$, $V_f = 1.5\,\text{m}^3$.
  • Work
    $W = P \Delta V = (3.6 \times 10^5)(1.5 - 1.0) = 1.8 \times 10^5\,\text{J}$ (180 kJ).
  • Change in internal energy
    $\Delta U = Q - W = 3.0 \times 10^5 - 1.8 \times 10^5 = 1.2 \times 10^5\,\text{J}$ (120 kJ).
• Practical insight
  • In real expansions/compressions, additional heat transfer may arise from frictional dissipation.

Ethical, Philosophical & Real-World Connections

• Energy bookkeeping (first law) underpins sustainability analyses: apparent “losses” (e.g., heat from engines, industrial processes) are merely transfers to less useful forms; guides efficiency improvements.
• Dietary Calories link thermodynamics to nutrition: biochemical energy released by metabolism measured in $\text{Cal}$ aligns with physical work/heat potential.
• Climate science leverages radiative heat transfer to model Earth’s energy balance; greenhouse effect alters how radiation exits, consistent with these principles.