Temperature, Thermometry, and Heat Transfer: Study Notes

1. Temperature & Thermometry

1a. Fundamental Concepts

Temperature and thermometry are foundational topics in thermodynamics, focusing on how energy is transferred and measured in physical systems.

• Conservation of Energy: Energy cannot be created or destroyed, only transferred or converted between forms.

• Heating/Cooling (Microscopic View): Faster/slower particle motion corresponds to internal energy changes.

• Observable Changes: Expansion, phase change, and pressure changes are macroscopic signs of energy transfer.

• Thermal Equilibrium: No net heat flow between two objects at the same temperature.

• Zeroth Law of Thermodynamics: If A and B are each in thermal equilibrium with C, then A and B are in thermal equilibrium with each other. This law forms the basis for defining temperature.

• Thermometers: Devices that use temperature-dependent physical properties (e.g., expansion, resistance, gas pressure) to measure temperature.

• Pressure Relation: $P = F/A$    1 atm = 1.01 \times 10^5$ Pa.

• Kelvin Scale: $T(\text{K}) = T(\degree \text{C}) + 273.15$

• Linear vs. Proportional: Linear = arithmetic, Proportional = passes origin ("y=mx").

1b. Thermal Expansion, Stress & Strain

Thermal expansion describes how materials change size with temperature. Stress and strain quantify deformation under force.

• Linear Expansion: $\Delta L = \alpha L_0 \Delta T$ $\Delta L$ = change in length, $\alpha$ = coefficient of linear expansion, $L_0$ = initial length, $\Delta T$ = temperature change.

• Volume Expansion: $\Delta V = \beta V_0 \Delta T$ $\beta$ = coefficient of volume expansion, $V_0$ = initial volume.

• Stress & Strain: $\sigma = F/A$, $\varepsilon = \Delta L / L_0$ $\sigma$ = stress, $F$ = force, $A$ = area, $\varepsilon$ = strain.

• Young's Modulus: $Y = \sigma / \varepsilon$ Measures stiffness of a material.

• Composite Materials: Different values for internal stress and strain (e.g., bimetallic strip).

2. Heat, Temperature & Phase Change

2a. Heat and Temperature

Heat is energy transferred due to temperature difference. Temperature is a measure of average kinetic energy of particles.

• Heat (Q): Energy transferred due to temperature difference.

• Specific Heat (c): $Q = mc\Delta T$ $m$ = mass, $c$ = specific heat capacity, $\Delta T$ = temperature change.

• Microscopic Reason: More degrees of freedom in a material result in higher specific heat.

• Phase Change: Temperature constant, $Q = mL$ $L$ = latent heat (fusion, vaporization, etc.).

• Equilibrium Systems: $\Sigma Q = 0$ in energy transfer problems.

• Heat Required (with phase change): Include $Q = mc\Delta T$ and $Q = mL$ as needed.

2b. Heat Flow: Conduction & Convection

Heat can be transferred by conduction (through materials) or convection (by fluid movement).

• Conduction (Heat Flow): $Q/t = kA\Delta T / L$ $k$ = thermal conductivity, $A$ = area, $\Delta T$ = temperature difference, $L$ = thickness.

• Thermal Resistance: $R = L/(kA)$, $Q = \Delta T / R$

• Series Layers: $R_{\text{total}} = R_1 + R_2 + \ldots$

• Convection: Heat is carried by fluid motion.

• Materials: Metals (good conductors) transfer heat faster than insulators (wood, plastic).

3. Practice & Application

3a. Example Problems

• Calibrated Thermometers: Why do they disagree at intermediate temperatures? (Consider calibration points and nonlinearity.)

• Heat Loss: Calculate heat loss through insulation, find current and interface temperature.

• Ice-Water Equilibrium: Find final temperature including phase change.

• Material Comparison: Why does metal feel colder than wood at the same temperature? (Metals conduct heat away from skin faster.)

• Heating Curve: Find specific heat and identify phase change point.

• Rod with $T(x)$ from 100 to 10°C: Find heat flow rate and interpret sign.

3b. Key Tips

• Focus on microscopic reasoning and unit conversions (J, Pa, K, W).

• Understand graphs: slope = heat capacity.

• Expect multi-step problems combining heat transfer and phase change.

4. Table: Comparison of Heat Transfer Methods

Method	Mechanism	Example
Conduction	Direct transfer through material	Metal rod heated at one end
Convection	Bulk movement of fluid	Boiling water circulating in a pot
Radiation	Electromagnetic waves	Sunlight warming the Earth

Additional info:

• Radiation is another mode of heat transfer, not covered in detail above but important in thermodynamics.

• Young's modulus, stress, and strain are key for understanding material deformation under thermal and mechanical loads.