Introductory Heat & Thermodynamics (PHY 102) – Comprehensive Bullet-Point Notes

Course Overview

  • Course Title & Code: Introductory Heat and Thermodynamics – PHY 102 (2 CU)

  • Prerequisites: High-school Physics & Mathematics

  • Broad Units Covered
    • Thermometry
    • Thermal Expansion
    • Heat Energy
    • Thermodynamics (1st & 2nd Laws, processes, Carnot cycle)
    • Cryogenics

  • Recommended Text: University Physics (15th ed.) by Young & Freedman

Topic 1 – Thermometry

  • 1.1 Temperature
    • Operational definition: proportional to average kinetic energy of particles
    • Measured in °C, K, °F
    • Zeroth Law: If A ↔ B and B ↔ C are in thermal equilibrium ⇒ A ↔ C. Provides logical foundation for temperature measurement and thermometer calibration.

  • 1.2 Thermometers & Observable Properties
    • Measurement device exploiting a temperature-dependent property:
    – Volume (liquid-in-glass, gas thermometers)
    – Electrical resistance (metal wire resistance thermometers)
    – Electromotive force (thermocouples)
    – Pressure (constant-volume gas thermometer)
    • Common types & principles
    – Mercury/alcohol liquid-in-glass: \Delta V of fluid
    – Gas thermometer: P \propto T at fixed volume
    – Resistance (RTD): R = R_0\left(1+\alpha\Delta T\right)
    – Thermocouple: Seebeck e.m.f. proportional to \Delta T
    – Digital/electronic sensors: semiconductor band-gap shift → voltage/frequency output.

  • 1.3 Temperature Scales
    • Celsius: based on 0\,°C (ice point) & 100\,°C (steam point).
    • Kelvin: absolute scale starting at absolute zero; TK = T{°C} + 273.15.
    • Fahrenheit: T{°F} = \tfrac{9}{5}T{°C} +32.
    • Conversions – worked examples (link to practice problems).

  • Illustrative Question Samples
    • Convert 30\,°C → K & °F.
    • A thermometer shows 100\,°F; find °C & K.
    • Name two physical properties used in thermometers.

Topic 2 – Thermal Expansion

  • Thermal agitation → increased inter-atomic spacing → macroscopic size change.

  • 2.1 Linear Expansion
    • Formula: \Delta L = \alpha L_0\Delta T
    • \alpha: linear coefficient ((\text{K}^{-1}) or °C⁻¹); typically 10^{-6}\text{–}10^{-5}\,\text{K}^{-1} for metals.
    • Practical example: bridges, rails, metal rods stretching.

  • 2.2 Volumetric Expansion
    • For isotropic solids/liquids: \Delta V = \beta V0\Delta T with \beta \approx 3\alpha. • Area expansion (sheets): \Delta A = 2\alpha A0\Delta T (useful for plate questions).

  • 2.3 Engineering/Everyday Applications
    • Expansion joints in bridges & railways prevent buckling.
    • Bimetallic strip thermostats bend due to differing \alpha values.
    • Gaps under metal lids/glass to accommodate \Delta V.

  • Practice Problems
    • Metal rod: L0 = 2\,\text{m}, \Delta L = 0.004\,\text{m} at \Delta T = 50\,°C → \alpha? • Metal sheet A0 = 1.5\,\text{m}^2, \alpha = 2\times10^{-5}/°C, \Delta T = 30\,°C → \Delta A.
    • Conceptual: why bridges need joints.

Topic 3 – Heat Energy

  • 3.1 Heat vs. Temperature
    • Heat Q: energy in transit due to \Delta T; unit J. 1 cal = 4.186 J.
    • Temperature: state variable, not energy quantity.

  • 3.2 Specific Heat Capacity c
    • Definition: heat required per kg for 1 K rise. Units \text{J·kg}^{-1}\text{K}^{-1}.
    • Formula: Q = mc\Delta T.
    • Water: high c = 4200\,\text{J·kg}^{-1}\text{K}^{-1} → climate moderation, coolant uses.
    • Example: 2 kg water, 20\rightarrow30\,°C: Q = 84\,000\,\text{J}.

  • 3.3 Latent Heat L
    • Heat for phase change at constant T.
    • Fusion Lf (solid↔liquid), vaporization Lv (liquid↔gas).
    • Equation: Q = mL.
    • Everyday significance: ice melts absorbing heat without warming; perspiration cooling.
    • Note: graph of T vs. heat shows plateau during phase change → constant T but increasing internal energy.

  • Sample Questions (reinforce laws)
    • Heat to raise 2 kg water from 20→100 °C?
    • Heat to melt 0.5 kg ice at 0 °C (given L_f)?
    • Define specific heat capacity & latent heat of fusion.

Topic 4 – Thermodynamics

4.1 First Law (Energy Conservation in Thermodynamic Form)

  • Statement: \Delta U = Q - W
    • \Delta U: internal energy change
    • Q: heat added (+) / removed (−)
    • W: work done by system (+ when expansion).

  • Work for piston-gas: W = P\Delta V (for constant P).

  • Consequences:
    • If Q>W ⇒ \Delta U>0 (heating or compression).
    • If W>Q ⇒ \Delta U<0 (cooling during expansion).

4.2 Quasi-Static Thermodynamic Processes

  • Isothermal (T = const)
    • \Delta U = 0 ⇒ Q = W.
    • Achieved via slow change with thermal reservoir.
    • Example: gas in bath slowly compressed.

  • Adiabatic (Q = 0)
    • \Delta U = -W.
    • Fast or perfectly insulated.
    • Expansion: T drops; compression: T rises.

  • Isochoric / Isovolumetric (V = const)
    • W = 0 ⇒ Q = \Delta U.
    • Rigid container heating.

  • Isobaric (P = const)
    • Q = \Delta U + W.
    • Example: boiling water at atmospheric pressure.

  • Practice & Concept Checks (selected)

    1. Gas expands isothermally, does 500 J work → Q = 500 J in.

    2. In isothermal expansion, internal energy? (unchanged).

    3. Adiabatic compression, \Delta U = +600 J → work done = −600 J (on gas).

    4. Isochoric heating of 2 kg gas, \Delta U = +800 J → W = 0.

    5. Isobaric heat in: 1200 J, work 300 J → \Delta U = 900 J.

4.3 Second Law (Directionality & Limits)

  • Clausius Statement: Heat does not flow spontaneously cold→hot.

  • Kelvin-Planck: Impossible to convert all heat from single reservoir into work (η<100%).

  • Entropy Statement: Total entropy of isolated system never decreases; increases for irreversible processes.

  • Entropy, S: measure of disorder; \Delta S = \frac{Q_{rev}}{T} for reversible path.

4.4 Heat Engines

  • Definition: Cyclic device converting heat QH from hot reservoir into work W while discarding QC to cold reservoir.

  • Energy balance: QH = W + QC; W = QH - QC.

  • Thermal efficiency: \eta = \frac{W}{QH} = 1 - \frac{QC}{Q_H} (always <1).

  • Ideal Limit – Carnot Engine • Reversible cycle with max efficiency: \eta{Carnot} = 1 - \frac{TC}{T_H} (K). • Four reversible steps:

    1. Isothermal expansion at T_H (heat in)

    2. Adiabatic expansion (T drops to T_C)

    3. Isothermal compression at T_C (heat out)

    4. Adiabatic compression (T rises to TH). • No engine surpasses Carnot efficiency for same TH, T_C.

  • Real-World Analogy: Car engine—fuel combustion provides QH, piston does W, exhaust heats air (big QC). Improving design aims to lower Q_C.

  • Sample Problems
    • Engine: QH = 600 J, QC = 400 J → \eta = 0.33 or 33 %.
    • Carnot at TH=500 K, TC=300 K → \eta_{max}= 1-\tfrac{300}{500}=0.40 (40 %).

Topic 5 – Cryogenics

  • Definition: Physics & technology of temperatures below −150 °C (123 K); includes liquefaction of gases, effects on materials.

  • Key Applications
    • Gas liquefaction (O₂, N₂, He): medical O₂ supply, rocket oxidizers.
    • Biological storage: blood, semen, ova; organ preservation.
    • Superconductivity & quantum computing: requires ≲10 K.
    • Space tech: propellant storage, IR detectors cooled for sensitivity.

  • Important Data: Nitrogen boils at 77\,\text{K} (−196 °C).

  • Practice Qs
    • Define cryogenics.
    • List two uses of cryogenic liquids.
    • At what T does N₂ liquefy? (77 K).

Consolidated Numerical Constants & Conversions

  • 1 cal = 4.186 J (food Calorie = 1000 cal).

  • Water c = 4200\,\text{J·kg}^{-1}\text{K}^{-1}.

  • Ice latent heat of fusion L_f = 334\,000\,\text{J·kg}^{-1}.

  • Liquid-to-gas latent heats: water L_v ≈ 2.26\times10^{6}\,\text{J·kg}^{-1}.

  • Typical \alpha metals: steel 1.2\times10^{-5}\,\text{K}^{-1}, aluminum 2.4\times10^{-5}\,\text{K}^{-1}.

Conceptual & Practical Connections

  • Climate & Engineering: High water c moderates coastal temperatures; expansion coefficients inform structural gaps.

  • Energy Technology: 2nd Law justifies real-world efficiency limits in power plants, motivates waste-heat recovery.

  • Medical Ethics: Cryogenic preservation raises debates on long-term viability & consent.

  • Sustainability: Understanding thermodynamic limits guides renewable-energy system design.

Study Strategy Tips

  • Memorize fundamental formulas in boxed form.

  • Practice unit conversions (°C↔K↔°F, grams↔kg, J↔cal).

  • Draw P$–$V diagrams for each thermodynamic process to visualize work (area under curve).

  • For efficiency questions, always track heat in, heat out, and sign conventions carefully.