Thermodynamics and Thermochemistry: Systems, State Functions, and Energy Changes

First Law of Thermodynamics

Introduction to the First Law

The first law of thermodynamics is a fundamental principle in chemistry and physics, stating that energy cannot be created or destroyed, only transformed from one form to another. In chemical systems, this law governs the changes in internal energy during reactions and physical processes.

• Mathematical Expression: The change in internal energy ($\Delta U$) of a system is equal to the heat ($q$) added to the system plus the work ($w$) done on the system.

$\Delta U = q + w$

• Energy In and Out: Energy can enter or leave a system as heat or work, but only changes in internal energy ($\Delta U$) are measurable, not absolute values.

• System Boundary: The boundary separates the system from its surroundings, and energy transfer occurs across this boundary.

Systems and Surroundings

Types of Systems

In thermodynamics, a system is the part of the universe we are interested in studying, such as a chemical reaction in a flask, an engine, or a battery. The surroundings are everything else outside the system.

• Open System: Both mass and energy can be exchanged with the surroundings (e.g., an open flask).

• Closed System: Only energy can be exchanged; mass remains constant (e.g., a sealed container).

• Isolated System: Neither mass nor energy is exchanged (e.g., a thermos bottle).

Example: A flask containing a chemical reaction is the system; the laboratory air is the surroundings.

Examples of Systems and Surroundings

• Atmospheric Processes: The Earth's atmosphere can be considered a system, with energy exchanges such as sunlight, heat emission, and greenhouse effects.

• Chemical Reactions: A beaker with dissolved chemicals is the system; the beaker and air are the surroundings.

• Physical Changes: Compression of a gas in a piston, where the gas is the system and the piston is part of the surroundings.

Heat and Temperature

Definitions and Concepts

Heat is the energy that flows into or out of a system due to a temperature difference between the system and its surroundings. Temperature is a measure of the average kinetic energy of the particles in a substance.

• Direction of Heat Flow: Heat flows from higher temperature to lower temperature until thermal equilibrium is reached.

• Formula for Kinetic Energy: The kinetic energy ($E_K$) of a moving object is given by:

$E_K = \frac{1}{2}mv^2$

• Example Calculation: For a person weighing 75.0 kg running at 1.78 m/s:

$E_K = \frac{1}{2} (75.0\,\text{kg}) (1.78\,\frac{\text{m}}{\text{s}})^2 = 119\,\text{J}$

Key Questions in Thermodynamics

• How is energy interconverted between different forms?

• Is a particular reaction or process possible at a certain temperature?

• How much useful work can be obtained from a reaction?

Thermochemistry

Heat and Chemical Reactions

Thermochemistry is the study of the heat energy involved in chemical reactions and physical changes. It applies the principles of thermodynamics to chemical processes.

• Exothermic Reaction: A reaction that releases heat to the surroundings. The reaction vessel gets hot.

• Endothermic Reaction: A reaction that absorbs heat from the surroundings. The reaction vessel gets cold.

General Reaction:

Exothermic: $A + B \rightarrow C + D + q$ Endothermic: $q + A + B \rightarrow C + D$

• Bond Breaking and Making: Bond breaking requires energy (endothermic), while bond formation releases energy (exothermic).

Examples

• Burning Firewood: Exothermic (releases heat).

• Burning Gas in Furnace: Exothermic (releases heat).

• Methane Combustion: $\text{CH}_4(g) + 2\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\text{H}_2O(l)$ Heat of reaction = –890 kJ (exothermic, heat is evolved).

State Variables and State Functions

Definitions

The state of a system is described by a set of variables, called state variables, such as pressure (P), volume (V), temperature (T), and amount of substance (n).

• State Function: A property that depends only on the current state of the system, not on the path taken to reach that state (e.g., internal energy, altitude).

• Path Function: A property that depends on the specific process or path taken (e.g., work, heat).

Classification of State Variables

Type	Examples	Dependence
Intensive	P, T	Independent of system size
Extensive	V, n, mass	Dependent on system size

Gravitational Potential Energy as a State Function

• Formula:

$E_{\text{potential}} = mgh$

• $m$ = mass (kg)

• $g$ = gravitational constant ($9.80\,\text{m}/\text{s}^2$)

• $h$ = height (m)

Gravitational potential energy is an extensive state function, as it depends on the mass and height of the object.

Summary

• Understanding the first law of thermodynamics is essential for analyzing energy changes in chemical systems.

• Systems and surroundings must be clearly defined to study energy transfer.

• Thermochemistry focuses on heat changes during chemical reactions, distinguishing between exothermic and endothermic processes.

• State variables and state functions are key concepts for describing the properties and changes of a system.

Practice Problems

• Review and solve textbook problems: 6.11, 6.31, 6.35, 6.97, 6.135 (10th edition).

Additional info: The notes cover topics from Chapter 6 (Thermochemical Aspects of Chemical Reactions) and foundational thermodynamics, relevant for General Chemistry.