PHY 102 – Thermal Physics Vocabulary

Course Overview

• PHY 102 (M) – Thermal Physics, Sound and Optics (3 Units)
  • Core areas announced on p. 1
  • Thermal Physics
    • Zeroth, First & Second Laws of Thermodynamics
    • Temperature, calorimetry, heat transfer, change of state, critical points
    • Gas laws, kinetic theory, black–body radiation
  • Sound
    • Production of sound by vibrating solids and air columns
    • Speed of sound in solids, liquids, gases
    • Intensity, pitch, quality; ear response; interference; Doppler effect
  • Optics
    • Reflection, absorption, spherical mirrors, thin lenses, combinations & aberrations
    • Optical instruments; resolving power of microscopes

Temperature & Zeroth Law of Thermodynamics

• Human sense of “hot/cold” is qualitative and often misleading (e.g.
  • Tile vs. carpet at same T feels different due to higher heat–transfer rate of tile)
• Need a quantitative property → temperature
• Zeroth Law statement
  • If bodies A and B are each in thermal equilibrium with body C, then A and B are in equilibrium with each other → they share a common temperature
• Consequences
  • Temperature is the property that determines heat-flow direction
  • Two bodies with different T will transfer energy until equilibrium is reached

Thermometers & Temperature Scales

• Thermometer principle: some physical property changes reproducibly with T
  • Examples: liquid volume, solid dimensions, gas pressure/volume, electrical resistance, colour
• Absolute (Kelvin) scale
  • Conversion: T_c = T - 273
• Fahrenheit vs. Celsius
  • Ice point: 32\,^\circ\text F ; steam point: 212\,^\circ\text F
  • Relationship: TF = \frac{9}{5}TC + 32
• Only Kelvin has a true zero; any formula involving ratios of temperatures must use kelvins
• Example conversion
  • 50\,^\circ\text F \Rightarrow 10\,^\circ\text C \text{ and } 283\,\text K

Thermal Expansion

• Linear expansion coefficient \alpha
  • Definition: \alpha = \frac{\Delta L}{L_i\,\Delta T}
  • Useful form: \Delta L = \alpha Li \Delta T = \alpha Li (Tf - Ti)
• Area & volume expansion (isotropic solids)
  • Area: \Delta A = 2\alpha A_i \Delta T
  • Volume: \Delta V = \beta V_i \Delta T where \beta = 3\alpha
• Example (railroad track)
  • (a) Find new length at 40\,^\circ\text C for a 30.000 m steel rail starting at 0\,^\circ\text C
  • (b) If clamped, quantify thermal stress (not numerically worked in transcript)

Quantity of Heat & Specific Heat Capacity

• Heat Q is energy transferred due to \Delta T between system & surroundings
• For a single phase: Q = mc\,(T - T_0)
  • c = specific heat capacity (J kg^{-1}\,^\circ\text C^{-1})
• Definition of c
  • c = \dfrac{Q}{m (T - T_0)}; low c ⇒ good thermal conductor; water chosen for engine cooling due to high c
• Example 1 (iron vat)
  • m = 20\,\text{kg},\; c_{\text{Fe}} = 450\,\text{J kg}^{-1}\,^\circ\text C^{-1}
  • \Delta T = 80\,^\circ\text C ⇒ Q = 7.2\times10^5\,\text J (720 kJ)
• Conservation of energy (calorimetry)
  • In isolated system: \text{heat lost} = \text{heat gained}

Calorimetry Examples

• Example 2 (tea + glass cup)
  • Tea: m=0.20\,\text{kg},\; c=4186\,\text{J kg}^{-1}\,^\circ\text C^{-1},\; T_i=95\,^\circ\text C
  • Glass cup: m=0.15\,\text{kg},\; c=840\,\text{J kg}^{-1}\,^\circ\text C^{-1},\; T_i=25\,^\circ\text C
  • Solve mt ct(95-T)=mc cc(T-25) ⇒ T \approx 89\,^\circ\text C
• Example 3 (specific heat of alloy)
  • Alloy: m=0.150\,\text{kg},\; T_i=540\,^\circ\text C
  • Water: 0.400\,\text{kg} at 10\,^\circ\text C
  • Aluminium calorimeter: 0.200\,\text{kg} at 10\,^\circ\text C
  • Equilibrium T_f=30.5\,^\circ\text C
  • Apply ms cs \Delta Ts = mw cw \Delta Tw + m{Al} c{Al} \Delta T{Al} ⇒ cs \approx 500\,\text{J kg}^{-1}\,^\circ\text C^{-1}

Phase Change & Latent Heat

• Specific latent heat L: energy per unit mass for a phase change at constant T
  • Fusion (solid↔liquid): L_f
  • Vaporization (liquid↔gas): Lv (greater than Lf because both internal + external work)
• Q = mL \;\Longrightarrow\; L = \dfrac{Q}{m}
• Example 4 (refrigerator)
  • Remove heat from 1.5 kg water at 20\,^\circ\text C to form ice at -12\,^\circ\text C
  • Q = m cw(20) + mLf + m c_{ice}(12) \approx 6.6\times10^5\,\text J (660 kJ)
• Heating curve notation (ice → water → steam)
  • Q1 = m c{ice}\,10; Q2 = m Lf; Q3 = m cw\,100; Q4 = m Lv

Newton’s Law of Cooling

• Rate proportional to excess temperature
  • \frac{dQ}{dt} \propto -(T - T_0)
  • \frac{dQ}{dt} = -k (T - T_0)

Heat-Transfer Mechanisms

• Conduction
  • Microscopic energy flow through matter, predominates in solids/metals
  • Fourier law: \frac{dQ}{dt} = -kA \frac{(T1 - T2)}{l}
  • k = thermal conductivity (large k ⇒ good conductor)
  • Example 5 (window)
  • Glass pane A = 3.0\,\text{m}^2,\; l = 3.2\,\text{mm},\; \Delta T = 1\,^\circ\text C
  • k_{glass} = 0.84\,\text{J s}^{-1}\,\text{m}^{-1\,^\circ\text C}^{-1} ⇒ \dot Q \approx 790\,\text W
• Convection
  • Bulk movement of fluid; much faster than conduction in fluids
  • Newton’s cooling analogue: \frac{dQ}{dt} = hA (T - T_0) with h = convection coefficient
• Radiation
  • Does not require medium; energy via electromagnetic waves
  • Stefan–Boltzmann law: \frac{dQ}{dt} = e\sigma A T^4
  • Net exchange between body (T$1$) and surroundings (T$2$):
    \frac{dQ}{dt} = e\sigma A (T1^4 - T2^4)
  • Example 6 (athlete)
  • A=1.5\,\text{m}^2,\; e=0.70,\; T{skin}=307\,\text K,\; T{wall}=288\,\text K
  • \dot Q \approx 120\,\text W

Kinetic Theory of Gases

• Assumptions
  1. Large number N of identical molecules, each mass m, random motion
  2. Mean separation ≫ molecule diameter ⇒ volume mostly empty
  3. Molecules obey classical mechanics; interact only via collisions
  4. Collisions with walls and each other are perfectly elastic
• Derivation highlights (cube side l)
  • Single molecule momentum change on wall: \Delta (mvx)=2mvx
  • Time between successive hits: \Delta t = \frac{2l}{v_x}
  • Force by one molecule: F = \frac{m v_x^2}{l}
  • Extend to N molecules, use average \overline{vx^2}; isotropy ⇒ \overline{vx^2}=\overline{vy^2}=\overline{vz^2}
  • v{rms}^2 = \overline{v^2} = 3\overline{vx^2}
  • Pressure: P = \frac{1}{3}\frac{N m \overline{v^2}}{V}
  • Combine with ideal-gas law PV = NkT ⇒
    \frac{1}{2} m \overline{v^2} = \frac{3}{2} kT
• Root-mean-square speed
  • v_{rms}=\sqrt{\overline{v^2}} = \sqrt{\frac{3kT}{m}} = \sqrt{\frac{3RT}{M}} (M = molar mass)
• Example 7: T=37\,^\circ\text C ⇒ \overline{KE} = \tfrac{3}{2}kT \approx 6.4\times10^{-21}\,\text J per molecule

Laws of Thermodynamics

Fundamental Concepts

• System: region/object under study
  • Closed: no mass flow; Open: mass can cross boundary
  • Isolated: no energy or mass exchange
• Internal energy U: microscopic energy content
• Heat (Q): energy transfer driven by \Delta T
• Work (W): energy transfer not driven by \Delta T (e.g.
  PdV mechanical work)

First Law (Energy conservation)

• \Delta Q = \Delta U + \Delta W
• Sign conventions (as used in transcript)
  • Q>0: heat added to system; Q<0: heat lost
  • W>0: work done by system; W<0: work done on system
• \Delta W = P \Delta V for quasi-static volume change
• Example 8
  • (a) Q=+2500\,\text J,\; W=-1800\,\text J ⇒ \Delta U = 4300\,\text J
  • (b) Q=+2500\,\text J,\; W=+1800\,\text J ⇒ \Delta U = 700\,\text J

Special Thermodynamic Processes

• Isothermal (\Delta T=0) for ideal gas
  • \Delta U=0 ⇒ \Delta Q = \Delta W
  • \Delta Q = P1V1 \ln!\left(\dfrac{V2}{V1}\right)
• Adiabatic (\Delta Q=0)
  • 0 = \Delta U + \Delta W ⇒ work comes at expense of internal energy
• Isochoric / isovolumic (\Delta V=0)
  • \Delta W=0 ⇒ \Delta Q = \Delta U
• Isobaric (P=\text{const})
  • Not explicitly derived, but work = P\Delta V

Second Law (directionality)

• Heat flows spontaneously from hot ⇒ cold, never cold ⇒ hot without external work
• Equivalent interpretations (not yet detailed: entropy, heat engines, etc.)

Additional Topics Mentioned (Preview)

• Critical points (phase diagrams)
• Black-body radiation
  • Planck law, Wien displacement, Stefan–Boltzmann already introduced via radiation section
• Sound
  • Vibrations of solids/air columns; speed formulas v=\sqrt{Y/\rho} (solids), v=\sqrt{B/\rho} (fluids)
  • Intensity I = P/A; decibel scale; interference & beats; Doppler effect f' = f\left(\dfrac{v\pm vo}{v\mp vs}\right)
• Optics
  • Reflection \thetai = \thetar; mirrors \dfrac{1}{f}=\dfrac{1}{do}+\dfrac{1}{di}
  • Thin-lens equation, combination of lenses \dfrac{1}{f{eq}}=\sum \dfrac{1}{fi}
  • Aberrations: spherical, chromatic
  • Resolving power d_{min}=1.22\dfrac{\lambda}{2NA} for microscopes (Rayleigh criterion)
• These sections are announced in syllabus and will be covered later; included for conceptual continuity.

Ethical & Practical Implications

• Engineering design must account for thermal expansion (e.g.
  rail gaps, bridge joints)
• High specific heat of water crucial for climate regulation & biological temperature stability
• Refrigeration and air-conditioning rely on large L_v for efficient heat removal
• Understanding radiative balance fundamental to climate science (Earth–Sun energy budget)
• Second-law directionality underpins efficiency limits of engines and informs sustainable energy systems