Chapter 17: Temperature and Heat – Structured Study Notes

Temperature and Heat

Introduction

Temperature and heat are fundamental concepts in thermodynamics, often confused in everyday language but distinct in physics. This chapter explores their definitions, measurement, and the physical processes associated with heat transfer and temperature change.

• Temperature is a measure of the average kinetic energy of particles in a substance.

• Heat is energy transferred between objects due to a temperature difference.

• Focus is on macroscopic objects; microscopic analysis follows in later chapters.

Thermal Equilibrium and Thermometers

Temperature and Thermal Equilibrium

Thermal equilibrium occurs when two systems in contact no longer exchange energy as heat.

• A thermometer measures temperature by exploiting physical properties that change with temperature (e.g., liquid volume).

• Two systems are in thermal equilibrium if and only if they have the same temperature.

Types of Thermometers

• Liquid-in-glass thermometers use the expansion of mercury or ethanol.

• Infrared thermometers measure radiation emitted from the skin, not direct contact.

The Zeroth Law of Thermodynamics

Statement and Implications

The zeroth law establishes the concept of temperature and thermal equilibrium.

• If system C is in thermal equilibrium with both A and B, then A and B are in thermal equilibrium with each other.

• This law allows the use of thermometers as reliable temperature indicators.

Temperature Scales

Celsius and Fahrenheit Scales

• Celsius (°C): 0°C is the freezing point, 100°C is the boiling point of water.

• Fahrenheit (°F): 32°F is the freezing point, 212°F is the boiling point of water.

• Conversion formulas:

• From Celsius to Fahrenheit: $T_F = \frac{9}{5}T_C + 32$

• From Fahrenheit to Celsius: $T_C = \frac{5}{9}(T_F - 32)$

Kelvin Scale and Absolute Zero

• Kelvin (K): Absolute temperature scale; 0 K is the temperature at which a gas exerts no pressure.

• Conversion from Celsius to Kelvin: $T_K = T_C + 273.15$

• Absolute zero: $-273.15^{\circ}C$ or 0 K, the lowest possible temperature.

Temperature Conversions Table

K	C	F
373	100	212
273	0	32
195	-78	-109
90	-183	-298
0	-273	-460

Thermal Expansion

Linear Thermal Expansion

Materials expand when heated due to increased atomic vibrations.

• Change in length: $\Delta L = \alpha L_0 \Delta T$ where $\alpha$ is the coefficient of linear expansion.

• Atoms behave like masses connected by springs; increased temperature increases average separation.

Volume Expansion and Expanding Holes

• Change in volume: $\Delta V = \beta V_0 \Delta T$ where $\beta = 3\alpha$ is the coefficient of volume expansion.

• Holes in objects expand as the object expands.

Coefficients of Linear and Volume Expansion

Material	α [K-1 or (°C)-1]
Aluminum	2.4 × 10-5
Brass	2.0 × 10-5
Copper	1.7 × 10-5
Glass	0.4–0.9 × 10-5
Invar	0.09 × 10-5
Quartz (fused)	0.04 × 10-5
Steel	1.2 × 10-5

Solids	β [K-1 or (°C)-1]
Aluminum	7.2 × 10-5
Brass	6.0 × 10-5
Copper	5.1 × 10-5
Glass	1.2–2.7 × 10-5
Invar	0.27 × 10-5
Quartz (fused)	0.12 × 10-5
Steel	3.6 × 10-5

Thermal Expansion of Water

• Between 0°C and 4°C, water decreases in volume as temperature increases (anomalous behavior).

• This causes lakes to freeze from the top down.

Thermal Stress

• If expansion/contraction is prevented, thermal stress develops.

• Force due to thermal stress: $F = Y\alpha A \Delta T$ where $Y$ is Young's modulus, $A$ is cross-sectional area.

• Expansion joints in bridges accommodate thermal expansion.

Heat and Calorimetry

Quantity of Heat

• Heat can be transferred by mechanical work or direct contact with a hotter body.

• Calorie (cal): Amount of heat required to raise 1 g of water from 14.5°C to 15.5°C.

Specific Heat

• Heat required to change temperature of mass $m$ by $\Delta T$:

• $Q = mc\Delta T$

• Specific heat $c$ varies by material; for water, $c \approx 4190$ J/kg·K.

Molar Heat Capacity

• Heat required to change temperature of $n$ moles by $\Delta T$:

• $Q = nC\Delta T$

• Molar heat capacity $C$ varies by material; for water, $C \approx 75.4$ J/mol·K.

Table: Specific Heats and Molar Heat Capacities

Substance	Specific Heat, c (J/kg·K)	Molar Mass, M (kg/mol)	Molar Heat Capacity, C (J/mol·K)
Aluminum	910	0.0270	24.6
Beryllium	1970	0.00901	17.7
Copper	390	0.0635	24.8
Ethanol	2448	0.0461	111.9
Water (liquid)	4190	0.0180	75.4

Phase Changes

Phases and Latent Heat

• Phases: solid, liquid, gas.

• Phase change: transition between phases; temperature remains constant during phase change.

• Latent heat $L$: heat per unit mass transferred during phase change.

• Heat for phase change: $Q = mL$

Heat of Fusion and Vaporization

• Heat of fusion: Energy required to melt a solid at its melting point.

• Example: Gallium melts at 29.8°C, $L_f = 8.04 \times 10^4$ J/kg.

• Heat of vaporization: Energy required to vaporize a liquid at its boiling point.

• Evaporation removes heat from the body, causing cooling.

Mechanisms of Heat Transfer

Overview

• Heat transfer occurs from higher to lower temperature objects.

• Three mechanisms: conduction, convection, radiation.

Conduction

• Occurs within or between solids in contact.

• Rate of heat transfer: $\frac{dQ}{dt} = kA \frac{T_H - T_C}{L}$ where $k$ is thermal conductivity, $A$ is area, $L$ is length.

Thermal Conductivities Table

Substance	k (W/m·K)
Silver	406
Copper	385
Aluminum	205
Wood	0.12–0.04
Concrete	0.8
Fiberglass	0.04
Styrofoam	0.027

Convection

• Transfer of heat by mass motion of fluid (liquid or gas).

• Example: Heating element in water causes convection currents.

Radiation

• Transfer of heat by electromagnetic waves (e.g., infrared, visible light).

• Stefan-Boltzmann law for heat current: $H = \lambda \epsilon \sigma T^4$ where $\lambda$ is area, $\epsilon$ is emissivity, $\sigma$ is Stefan-Boltzmann constant, $T$ is absolute temperature.

Radiation and Climate Change

• Earth's surface radiates energy mainly as infrared.

• CO2 in the atmosphere absorbs and reradiates infrared, contributing to global warming.

Summary Table: Key Equations

Concept	Equation (LaTeX)
Celsius to Fahrenheit	$T_F = \frac{9}{5}T_C + 32$
Fahrenheit to Celsius	$T_C = \frac{5}{9}(T_F - 32)$
Celsius to Kelvin	$T_K = T_C + 273.15$
Linear Expansion	$\Delta L = \alpha L_0 \Delta T$
Volume Expansion	$\Delta V = \beta V_0 \Delta T$
Thermal Stress	$F = Y\alpha A \Delta T$
Specific Heat	$Q = mc\Delta T$
Molar Heat Capacity	$Q = nC\Delta T$
Latent Heat	$Q = mL$
Conduction	$\frac{dQ}{dt} = kA \frac{T_H - T_C}{L}$
Radiation	$H = \lambda \epsilon \sigma T^4$

Example Applications

• Railroad tracks: Gaps are left to accommodate thermal expansion and prevent buckling.

• Bridges: Expansion joints prevent structural damage due to temperature changes.

• Climate change: Increased atmospheric CO2 leads to higher global temperatures by trapping infrared radiation.

Additional info: All equations and tables have been expanded and clarified for academic completeness. The notes are structured to cover all major subtopics in Chapter 17, suitable for college-level physics exam preparation.