Thermochemistry & Heat Transfer Fundamentals

Energy: Forms & Definitions

• Kinetic Energy vs. Temperature
  • Temperature ≈ average kinetic energy of particles.
  • Small particles can move faster than large ones yet have similar average KE.
• Thermal Energy
  • KE of particles due to random motion at the atomic / molecular level.
• Stored (Potential) Energies relevant to chemistry
  • Nuclear energy: energy holding protons & neutrons; released in nuclear reactions.
  • Chemical energy: energy stored in electrostatic attractions (ionic) or covalent bonds; accessed in chemical reactions.
  • Gravitational potential energy is negligible at atomic scale.
• Scope of course: focus on thermal & chemical energies; others mentioned only for context.

Systems, Surroundings, & Energy Flow

• System: the specific substance(s) studied (e.g.
  • Reactants/products in a reaction.
  • Ice cube undergoing phase change).
• Surroundings: everything in thermal contact with system (beaker, air, water bath, etc.).
• Energy Conservation
  • Energy absorbed by system = energy lost by surroundings.
  • Endothermic: system absorbs heat (q>0).
  • Exothermic: system releases heat (q<0).

Heat Transfer Principles

• Heat (q) always flows high → low temperature.
  • You cannot "give cold"; only remove heat.
• Two objects at identical T may still exchange energy differently because their heat capacities differ.
• Identical heat exposure → different ΔT for different materials (sand vs. water, concrete vs. pool water).

Temperature, Energy & Measurement Limits

• No instrument measures internal energy directly; we infer via temperature change.
• Direct relationship: add heat → particles move faster → T rises (and vice-versa).
• Factors controlling ΔT when heat is added/removed:
  1. Mass (m) of substance.
  2. Amount of heat (q) supplied/removed.
  3. Identity of substance (specific heat c).

Specific Heat Capacity (c)

• Definition: energy needed to raise 1 g of a substance by 1 °C.
  c = \frac{q}{m\,\Delta T}\;\left(\frac{J}{g\,^{\circ}C}\right)
• Typical values
  • Water: c{H2O}=4.184\,\frac{J}{g\,^{\circ}C} (high → heats/cools slowly).
  • Iron: c_{Fe}\approx0.45\,\frac{J}{g\,^{\circ}C} (low → heats/cools quickly).

Quantitative Relationship: q = mc\,\Delta T

• Variables
  • q = heat (J or kJ)
  • m = mass (g)
  • c (or s) = specific heat (J g⁻¹ °C⁻¹)
  • \Delta T = T{final}-T{initial} (°C). Sign matters!
  • \Delta T>0 \Rightarrow q>0 (endothermic)
  • \Delta T<0 \Rightarrow q<0 (exothermic)

Sample Problem Worked in Lecture

• "A sample of water absorbs 21.3\,\text{kJ} as its temperature rises from 18.0\,^{\circ}C to 76.2\,^{\circ}C. Find the mass."
• Convert heat to joules: q=21.3\,\text{kJ}=21300\,J.
• Calculate ΔT: \Delta T = 76.2-18.0 = 58.2\,^{\circ}C.
• Solve for m:
  m = \frac{q}{c\,\Delta T}=\frac{21300}{4.184\times58.2}\;\text{g}\approx87.5\,g.
• Negative answers signal algebra/sign error (use as quick check).

Real-World / Classroom Examples

• Cooking: heating pan + food (system) with stovetop (surroundings).
• Ice cube melting: ice absorbs heat from air/table until phase change.
• Beach vs. Water: sand/concrete reach high T quickly; water resists T change → milder coastal climates.
• Beaker reaction: chemicals (system) vs. beaker + solution (surroundings).

Practical & Conceptual Takeaways

• Heat flows spontaneously toward equilibrium (2nd law context).
• Specific heat explains climate effects, material design (fire-resistant concrete, cookware, thermal buffers).
• Sign convention (+/−) in q = mc\Delta T connects algebra to thermodynamic meaning (absorbed vs. released heat).
• Mass & material identity must be known for precise calorimetry.

Problem-Solving Checklist

1. List knowns: q, m, c, \Delta T.
2. Ensure units (kJ → J, g, °C).
3. Compute \Delta T= Tf-Ti; keep sign.
4. Rearrange q=mc\Delta T for unknown.
5. Check sign/units; negative mass or heat flags mistake.
6. Interpret: positive q → endothermic, negative → exothermic.

Reference Values & Constants (commonly used)

• c{H2O}=4.184\,J\,g^{-1}\,^{\circ}C^{-1}
• c_{Fe}\approx0.45\,J\,g^{-1}\,^{\circ}C^{-1}
• 1 kJ = 10^3 J

These bullet-point notes consolidate every concept, example, definition, numerical figure, and algebraic relation from the transcript, ready for exam review or problem practice.