Chapter 19: Work, Heat, and the First Law of Thermodynamics – Study Notes

Work, Heat, and the First Law of Thermodynamics

Introduction to the First Law of Thermodynamics

The first law of thermodynamics is a fundamental principle of energy conservation in physics. It states that the change in a system’s thermal energy is equal to the sum of energy transferred as work and as heat. This law is crucial for understanding energy exchanges in physical systems, especially in thermodynamic processes.

• First Law Equation: $\Delta E_{th} = W + Q$

• Energy Conservation: Energy cannot be created or destroyed, only transferred or transformed.

• Applications: Used in engines, power plants, and spacecraft.

Energy Transfer: Work and Heat

Energy can be transferred to or from a system either as work or as heat. Work is associated with mechanical interactions, while heat is associated with thermal interactions due to temperature differences.

• Work (W): Transfer of energy via mechanical means (forces causing displacement).

• Heat (Q): Transfer of energy due to temperature difference between system and environment.

• Sign Conventions:

  • W > 0: Energy added to system (compression)

  • W < 0: Energy extracted from system (expansion)

  • Q > 0: Energy added (environment hotter than system)

  • Q < 0: Energy extracted (system hotter than environment)

Mechanisms of Heat Transfer

Heat can be transferred between a system and its environment through several mechanisms:

• Conduction: Direct transfer through material.

• Convection: Transfer via fluid motion.

• Radiation: Transfer via electromagnetic waves.

• Evaporation: Transfer via phase change.

Thermal Properties of Matter

Materials respond to heat in ways governed by their thermal properties, such as specific heat, heat of fusion, heat of vaporization, and thermal conductivity. Calorimetry is the process of determining final temperature when systems interact thermally.

• Specific Heat (c): Energy required to raise 1 kg of substance by 1 K.

• Heat of Fusion (Lf): Energy required for phase change (solid to liquid).

• Heat of Vaporization (Lv): Energy required for phase change (liquid to gas).

• Thermal Conductivity (k): Measure of how well a material conducts heat.

Energy Review and Conservation

The total energy of a system includes both macroscopic (mechanical) and microscopic (thermal) energy. For isolated systems, the total energy remains constant.

• Energy Equation: $\Delta E_{sys} = \Delta E_{mech} + \Delta E_{th} = W_{ext}$

• Isolated System: $W_{ext} = 0$ implies constant total energy.

Work in Ideal-Gas Processes

Work Done on a Gas

Work is done on a gas by changing its volume, typically using a piston. The mathematical expression for work in an ideal-gas process is:

• Work Formula: $W = - \int_{V_i}^{V_f} p \, dV$

• Geometric Interpretation: Work equals the negative area under the pV curve.

Sign of Work

The sign of work depends on whether the gas is compressed or expanded:

• Compression: W > 0 (energy added)

• Expansion: W < 0 (energy extracted)

Special Ideal-Gas Processes

There are three important types of ideal-gas processes:

• Isochoric Process: Volume constant, no work done ($W = 0$)

• Isobaric Process: Pressure constant, work done is $W = -p \Delta V$

• Isothermal Process: Temperature constant, work done is $W = -nRT \ln \left( \frac{V_f}{V_i} \right)$

Heat, Temperature, and Thermal Energy

Definitions and Relationships

Thermal energy is the energy due to the motion of atoms and molecules. Heat is energy transferred between system and environment, and temperature quantifies the system’s “hotness.”

• Thermal Energy (Eth): Microscopic energy of moving molecules.

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

• Temperature (T): State variable indicating thermal state.

Units of Heat

The SI unit of heat is the joule (J). Historically, the calorie was used:

• 1 cal = 4.186 J

• 1 food Calorie = 1 kcal = 4186 J

Understanding Work and Heat

Work and heat are two distinct ways of transferring energy. The following table summarizes their differences:

	Work	Heat
Interaction	Mechanical	Thermal
Requires	Force & displacement	Temperature difference
Process	Macroscopic pushes/pulls	Microscopic collisions
Positive value	W > 0: Compression	Q > 0: Environment hotter
Negative value	W < 0: Expansion	Q < 0: System hotter
Equilibrium	Mechanical equilibrium	Thermal equilibrium

Specific Heat and Calorimetry

Specific Heat

Specific heat is the amount of energy required to raise the temperature of a unit mass (or mole) of a substance by one degree.

• Formula: $Q = Mc \Delta T$ (mass-specific)

• Molar Specific Heat: $Q = nC \Delta T$

Table: Specific Heats of Various Materials

Substance	c (J/kg K)	C (J/mol K)
Aluminum	900	24.3
Copper	385	24.4
Iron	449	25.1
Gold	129	25.4
Lead	128	26.5
Ice	2090	37.6
Ethyl alcohol	2400	110.4
Mercury	140	28.1
Water	4190	75.4

Calorimetry

Calorimetry is the study of heat transfer between interacting systems. When two or more systems interact thermally, they reach a common final temperature.

• Energy Conservation: $Q_{net} = Q_1 + Q_2 + ... = 0$

Phase Changes and Heat of Transformation

Phase Change

During a phase change, thermal energy changes without a change in temperature. The heat required for a phase change is given by:

• Formula: $Q = ML$

• Heat of Fusion (Lf): Melting/freezing

• Heat of Vaporization (Lv): Boiling/condensing

Table: Melting/Boiling Temperatures and Heats of Transformation

Substance	Tm (°C)	Lf (J/kg)	Tb (°C)	Lv (J/kg)
Nitrogen (N2)	-210	0.26 × 105	-196	1.99 × 105
Ethyl alcohol	-114	1.09 × 105	78	8.79 × 105
Mercury	-39	0.11 × 105	357	2.96 × 105
Water	0	3.33 × 105	100	22.6 × 105
Lead	328	0.25 × 105	1750	8.58 × 105

Heat Transfer Mechanisms

Conduction

Conduction is the transfer of heat through a material. The rate of heat transfer is given by:

• Formula: $\frac{dQ}{dt} = kA \frac{\Delta T}{L}$

• Thermal Conductivity (k): Higher k means better conduction.

Table: Thermal Conductivities

Material	k (W/m K)
Diamond	2000
Silver	430
Copper	400
Aluminum	240
Iron	80
Stainless steel	14
Ice	1.7
Concrete	0.8
Glass	0.8
Styrofoam	0.035
Air (20°C, 1 atm)	0.023

Convection

Convection is the transfer of thermal energy by the motion of fluids. Heated fluid becomes less dense and rises, while cooler fluid sinks.

Radiation

Radiation is the transfer of energy via electromagnetic waves. The rate of heat transfer by radiation is:

• Formula: $\frac{dQ}{dt} = e \sigma A T^4$

• Emissivity (e): Ranges from 0 (no emission) to 1 (perfect emitter).

• Stefan-Boltzmann Constant (σ): $5.67 \times 10^{-8}$ W/m2K4

Summary of Basic Gas Processes

Summary Table: Basic Gas Processes

Process	Work (W)	Heat (Q)	Thermal Energy Change (ΔEth)
Isothermal	Nonzero	Nonzero	0
Isochoric	0	Nonzero	Nonzero
Adiabatic	Nonzero	0	Nonzero

Important Concepts and Equations

• First Law: $\Delta E_{th} = W + Q$

• Work in Ideal-Gas Processes: $W = - \int_{V_i}^{V_f} p \, dV$

• Calorimetry: $Q_{net} = Q_1 + Q_2 + ... = 0$

• Adiabatic Process: $pV^{\gamma} = \text{constant}$, $\gamma = \frac{C_P}{C_V}$

• Heat of Transformation: $Q = ML$

• Specific Heat: $Q = Mc \Delta T$

• Molar Specific Heat: $Q = nC \Delta T$

• Conduction: $\frac{dQ}{dt} = kA \frac{\Delta T}{L}$

• Radiation: $\frac{dQ}{dt} = e \sigma A T^4$

Additional info: These notes expand on the preview and summary slides, providing definitions, formulas, and examples for each major concept in Chapter 19. All tables are recreated for clarity and completeness. Images are included only where they directly reinforce the explanation.