Thermal Energy, Specific Heat Capacity & Thermodynamics Study Notes

Fundamental Concepts

• Thermal / Internal Energy
  • Total microscopic energy stored in a system.
  • Sum of kinetic energy (motion of particles) + potential energy (inter-particle forces).
  • Increase in thermal energy ⇒ increase in internal energy, particle speed or separation.
• Heat vs. Temperature
  • Heat = energy in transit due to temperature difference; measured in $\text{J}$.
  • Temperature = measure of average kinetic energy of particles; unit Kelvin (K).
  • Absolute zero $0\,\text{K}\,(!!-273\,^{\circ}\text{C})$: particles possess essentially no kinetic energy.
  • Conversion: $T<em>{\text{(K)}} = T</em>{\,(^{\circ}\text{C})} + 273$.

Laws of Thermodynamics

• Zeroth Law
  • If body A is in thermal equilibrium with body B, and B with C, then A and C are also in thermal equilibrium.
  • Foundation for the definition of temperature.
• First Law (Energy Conservation for Thermodynamic Systems)
  • $\Delta U = Q + W$
    • $\Delta U$: change in internal energy.
    • $Q$: heat supplied to the system (positive when added).
    • $W$: work done by the system on surroundings (positive when done by the system in transcript convention).
• Second Law
  • Heat flows spontaneously from higher to lower temperature objects until equilibrium is reached.
  • Implies real processes have irreversibilities (friction, sound), limiting efficiency.

Specific Heat Capacity (SHC)

• Definition
  • Energy required to raise the temperature of $1\,\text{kg}$ of a substance by $1\,^{\circ}\text{C}$ (or $1\,\text{K}$) without a phase change.
• Equation
  • $Q = mc\,\Delta T$
    • $m$: mass (kg)
    • $c$: specific heat capacity $(\text{Jkg}^{-1}\text{K}^{-1})$
    • $\Delta T$: temperature change (K or $^{\circ}\text{C}$).
• Value for water: $c_{\text{water}} = 4.18 \times 10^{3}\,\text{Jkg}^{-1}\text{K}^{-1}$.
• Key ideas
  • Large $c$ ⇒ substance can ‘hold’ lots of heat with small temperature change (thermal buffering).
  • No change of state occurs during SHC processes.

Specific Latent Heat (SLH)

• Definition
  • Energy required to change the state of $1\,\text{kg}$ of a substance at constant temperature.
• Types & Symbols
  • Fusion (solid ↔ liquid): $L_f$.
  • Vaporisation (liquid ↔ gas): $L_v$.
• Equation
  • $Q = mL$.
• Units: $\text{Jkg}^{-1}$.
• Example: Steam at $100^{\circ}\text{C}$ contains more energy than water at $100^{\circ}\text{C}$ because of the latent heat of vaporisation.

Energy Transfer Mechanisms

• Conduction: particle-to-particle transfer in solids.
• Convection: bulk movement of fluids (liquids & gases).
• Radiation: emission/absorption of electromagnetic waves; no particles required.

Temperature–Time Graphs

• Flat regions ⇒ latent heat (energy in, temperature constant).
• Sloped regions ⇒ SHC processes (temperature changes, no phase change).
• Gradient in sloped region linked to $c$; length of plateaus linked to $L$.

Internal Energy & Kinetic Model Connections

• In thermal equilibrium, two bodies share the same temperature ⇒ same average kinetic energy per particle.
• Microscopic picture explains conduction (vibrations), convection (density changes), radiation (photon emission).

Efficiency of Machines

• Formula
  • $\eta = \dfrac{\text{useful energy\,out}}{\text{total energy\,in}} \times 100\%$.
• Sources of loss: friction, sound, electrical resistance.
• Improvement strategies
  • Use lubricants to minimise friction.
  • Employ low-resistance wiring.
  • Reduce vibration of moving parts.
  • Streamline vehicles to cut drag.

Experimental Considerations & Mandatory Practicals

• Determining SHC in the lab
  1. Measure mass $m$ of sample.
  2. Supply known electrical energy $Q = IVt$ or $Q = P t$.
  3. Record initial and final temperatures to get $\Delta T$ with a calibrated probe.
  4. Compute $c = \dfrac{Q}{m\,\Delta T}$.
  5. Plot scatter graph of $Q$ vs $\Delta T$; gradient $= mc$.
  6. Estimate absolute & percentage uncertainties; include error bars, find gradient uncertainty.
  7. Repeat trials to obtain means & reduce random error; comment on systematic errors (heat loss to surroundings).
• Risk assessment: hot surfaces, electrical hazards, steam burns—implement goggles, heat-resistant gloves, circuit fuses.

Key Equations & Constants (Quick Reference)

• $\Delta U = Q + W$ (First Law)
• $Q = mc\,\Delta T$ (Specific Heat Capacity)
• $Q = mL$ (Specific Latent Heat)
• $\eta = \dfrac{\text{useful}\;E<em>{\text{out}}}{E</em>{\text{in}}} \times 100\%$ (Efficiency)
• $T<em>{\text{(K)}} = T</em>{\,(^{\circ}\text{C})} + 273$ (Kelvin conversion)
• $c_{\text{water}} = 4.18 \times 10^{3}\,\text{Jkg}^{-1}\text{K}^{-1}$

Real-World & Theoretical Links

• Appliances: kettles, engines—design revolves around SHC, SLH, and efficiency constraints.
• Climate science: water’s high $c$ moderates Earth’s temperature.
• Industrial processes: latent heat exploited in distillation, refrigeration.
• Absolute zero concept underpins cryogenics & quantum research.