Laws of Thermodynamics

The First Law of Thermodynamics

The First Law of Thermodynamics is also called the Law of Conservation of Energy. It states that energy cannot be created or destroyed, but can be converted from one form to another. The total energy of the universe remains constant.

Think of energy like money in a closed bank account. You cannot create new money from nothing, and money doesn’t disappear. You can only transfer it between savings and current accounts, or convert it to different forms (cash, mobile money), but the total amount stays the same.

Mathematical Expression:

ΔU = q + w

Where:
ΔU = Change in internal energy of the system (energy stored in molecules)
q = Heat absorbed by the system (positive if absorbed, negative if released)
w = Work done on the system (positive if done on system, negative if done by system)

Understanding the Components:

Internal Energy (U): This is all the energy stored inside a substance. It includes kinetic energy from moving molecules and potential energy from bonds between atoms. You cannot measure U directly, but you can measure changes in it (ΔU).

Heat (q): Heat is energy transferred because of temperature difference. When you heat water in a kettle, energy flows from the hot element to cooler water. If a system absorbs heat, q is positive. If it releases heat, q is negative.

Work (w): Work involves energy transfer through movement against a force. In chemistry, this usually means gas expansion or compression. When gas expands and pushes against atmospheric pressure (like in a car engine), the system does work on the surroundings, so w is negative. When you compress gas (like pumping a tire), work is done on the system, so w is positive.

Sign Conventions (Important for WAEC):

Practical Example:

When petrol burns in a car engine, chemical energy converts to heat and work. The heat warms the engine (some energy is lost), while the expanding gases do work by pushing the pistons. The total energy from the petrol equals the sum of heat released and work done. No energy disappears or appears from nothing.

The Second Law of Thermodynamics

The Second Law of Thermodynamics states that natural processes tend to increase the total entropy (disorder) of the universe. In simpler terms, things naturally become more disorganized unless you add energy to organize them.

Mathematical Expression:

ΔS_universe ≥ 0

or more specifically:

ΔS_universe = ΔS_system + ΔS_surroundings ≥ 0

Where:
ΔS = Change in entropy (measure of disorder)
ΔS_universe must always be zero or positive for any real process

Understanding Entropy:

Entropy (S) measures the disorder or randomness in a system. High entropy means high disorder. Think of a neat classroom at the start of the day versus the same classroom after break time. Without effort to organize (add energy), disorder naturally increases.

Examples of Increasing Entropy:

• Ice melting to water (ordered solid → less ordered liquid)
• Water evaporating to steam (liquid → highly disordered gas)
• Sugar dissolving in water (organized crystals → scattered molecules)
• Gas expanding into a vacuum (concentrated → spread out)
• A hot object cooling down (concentrated energy → dispersed energy)

In all these examples, molecules become more randomly distributed. Nature favors this increased disorder.

Why Does Entropy Increase?

There are many more ways to be disordered than to be ordered. Imagine throwing 100 naira notes in the air. They could land in a neat stack (one way, very ordered), or scattered everywhere (millions of ways, disordered). Random processes naturally lead to the more probable disordered states.

Implications of the Second Law:

• Heat flows from hot to cold: This increases entropy because energy spreads out.
• Perfect engines are impossible: You cannot convert 100% of heat to work because some energy must disperse (increase entropy).
• Reactions have direction: Spontaneous reactions increase total entropy of universe.
• You can decrease entropy locally: Freezing water decreases entropy of water, but the surroundings gain more entropy from released heat. Total entropy still increases.

The Third Law of Thermodynamics

The Third Law of Thermodynamics states that the entropy of a perfect crystal at absolute zero (0 K or -273°C) is exactly zero.

Mathematical Expression:

S = 0 at T = 0 K (for perfect crystals)

This law provides a reference point for measuring absolute entropy values. At absolute zero, molecules have minimum possible energy and are perfectly ordered in a crystal structure. This is the state of zero disorder.

Key Points:

• Absolute zero (0 K = -273.15°C) is the lowest possible temperature
• At this temperature, molecular motion stops (theoretically)
• Perfect order exists – all molecules in exact positions
• We can calculate absolute entropy values for any substance at any temperature using this reference
• Absolute zero cannot actually be reached (only approached very closely)

This law is less commonly tested in WAEC but provides the foundation for calculating entropy changes in reactions.

Gibbs Free Energy: Connecting the Laws

The Laws of Thermodynamics combine in the Gibbs Free Energy equation, which predicts whether reactions occur spontaneously.

ΔG = ΔH – TΔS

Where:
ΔG = Change in Gibbs free energy
ΔH = Change in enthalpy (heat content)
T = Temperature in Kelvin
ΔS = Change in entropy

Interpreting ΔG:

• ΔG < 0 (negative): Reaction is spontaneous (happens on its own)
• ΔG = 0: System is at equilibrium (no net change)
• ΔG > 0 (positive): Reaction is non-spontaneous (needs external energy)

Relationship with Equilibrium Constant:

ΔG° = -RT ln K

Where:
ΔG° = Standard free energy change
R = Gas constant (8.314 J/mol·K)
T = Temperature in Kelvin
K = Equilibrium constant
ln = Natural logarithm

This equation connects thermodynamics to chemical equilibrium. Large negative ΔG° means large K, so products are strongly favored at equilibrium.

Comparison of Thermodynamic Functions

Applications in Real Life

1. Refrigerators and Air Conditioners: These devices use thermodynamic principles to move heat from cold to hot (opposite of natural flow). They require work input (electricity) because this decreases entropy locally, so you must increase entropy elsewhere to satisfy the Second Law.

2. Power Stations: Coal or gas power stations convert chemical energy to electrical energy. The First Law ensures energy is conserved. The Second Law explains why not all heat converts to electricity – some must disperse to increase entropy, reducing efficiency.

3. Photosynthesis: Plants decrease their own entropy by organizing CO₂ and H₂O into ordered glucose molecules. This is possible because they absorb energy from the sun. The sun’s entropy increases much more, so total entropy increases.

4. Spontaneous Reactions: Rusting of iron happens spontaneously because ΔG is negative. Even though rust formation releases heat (exothermic), the entropy increase from forming more particles drives the process.

Common Exam Mistakes

WAEC examiners regularly report these errors:

• Confusing ΔU, ΔH, and ΔG: Students mix up internal energy (U), enthalpy (H), and Gibbs free energy (G). Remember: ΔG = 0 at equilibrium, not ΔU or ΔH.
• Wrong signs for q and w: Many students get confused about when q and w are positive or negative. Remember: heat IN and work ON the system are positive.
• Saying entropy always increases: Entropy of the universe always increases, but entropy of a system can decrease if surroundings gain more entropy. Students forget to consider total entropy.
• Claiming energy is lost: Students write that energy is “lost as heat.” Energy is never lost – it is conserved (First Law). Energy can be transferred or dispersed, but not lost.
• Misinterpreting spontaneous: Students think spontaneous means fast. Spontaneous only means thermodynamically favorable (ΔG < 0). Diamond converting to graphite is spontaneous but extremely slow.
• Forgetting Kelvin temperature: In all thermodynamic equations, temperature must be in Kelvin, not Celsius. Students often forget to convert.
• Confusing ΔG and ΔG°: ΔG° is at standard conditions (1 atm, 298 K, 1 M). ΔG is at actual conditions. They are related but different.

Practice Questions

Multiple Choice Questions

1. Which statement correctly describes the First Law of Thermodynamics?

• Energy flows from hot to cold objects
• Entropy of the universe is constantly increasing
• Energy cannot be created or destroyed ✓
• Spontaneous processes have negative free energy

(Answer: c – This is the Law of Conservation of Energy)

2. A gas expands and does 500 J of work on the surroundings. The system also absorbs 300 J of heat. What is the change in internal energy (ΔU)?

• +800 J
• +200 J
• -200 J ✓
• -800 J

(Answer: c – ΔU = q + w = (+300 J) + (-500 J) = -200 J. Work done BY system is negative)

3. Which process shows an increase in entropy?

• Water freezing to ice
• CO₂(g) changing to dry ice CO₂(s)
• Condensation of steam to water
• Dissolving salt in water ✓

(Answer: d – Ions spreading throughout solution increases disorder. All others involve molecules becoming more ordered)

4. For a reaction at equilibrium, which statement is true?

• ΔH = 0
• ΔS = 0
• ΔG = 0 ✓
• ΔU = 0

(Answer: c – At equilibrium, Gibbs free energy change is zero)

Essay Questions

1. (a) State the First Law of Thermodynamics. (2 marks)
(b) Explain the meaning of each term in the equation: ΔU = q + w (6 marks)
(c) A system absorbs 800 J of heat and has 300 J of work done on it. Calculate the change in internal energy of the system. (3 marks)
(d) Give two practical applications of the First Law of Thermodynamics. (2 marks)

Tips: In part (b), clearly define each symbol and explain the sign conventions. Show all steps in part (c) calculations. Remember work done ON system is positive.

2. (a) State the Second Law of Thermodynamics. (2 marks)
(b) Define entropy and explain why natural processes tend to increase entropy. (4 marks)
(c) For each of the following processes, state whether entropy increases or decreases, giving reasons:
(i) Ice melting to water
(ii) Formation of ammonia from nitrogen and hydrogen gases
(iii) Dissolving sugar in tea
(iv) Condensation of water vapor (8 marks)
(d) Explain why you can freeze water even though it decreases the entropy of water. (3 marks)

Tips: In part (c), consider whether molecules become more spread out (gases) or more ordered (solids). For part (d), discuss total entropy change including surroundings.

3. (a) Write the equation relating Gibbs free energy (ΔG) to enthalpy (ΔH) and entropy (ΔS). (2 marks)
(b) Explain what each symbol in the equation represents. (4 marks)
(c) State the conditions for a reaction to be:
(i) Spontaneous
(ii) At equilibrium
(iii) Non-spontaneous (3 marks)
(d) A reaction has ΔH = -50 kJ/mol and ΔS = -100 J/mol·K. Will this reaction be spontaneous at 298 K? Show your working. (R = 8.314 J/mol·K) (4 marks)
(e) Write the equation connecting ΔG° to the equilibrium constant K. (2 marks)

Tips: Convert units carefully (kJ to J). Temperature must be in Kelvin. Show all calculation steps clearly. Negative ΔG means spontaneous.

Memory Aids

First Law: “Energy is Forever” – Energy cannot be created or destroyed, it lasts forever in the universe.

Second Law: “Disorder Dominates” – Natural processes increase disorder (entropy).

Sign Convention for q and w: “In and On are Positive” – Heat IN and work ON the system are positive.

Entropy Order: “Gas > Liquid > Solid” – Gases have highest entropy, solids have lowest.

Spontaneity: “Negative is Go” – Negative ΔG means reaction is spontaneous (go ahead).

ΔG equation: “Girls Have Tiny Shoes” – ΔG = ΔH – TΔS (silly but memorable!)

Related Topics

Understanding thermodynamics connects to these important chemistry topics:

• Chemical Equilibrium: ΔG = 0 defines equilibrium state
• Reaction Kinetics: Thermodynamics tells if reaction is possible, kinetics tells how fast
• Electrochemistry: Free energy relates to cell potential in batteries
• Phase Changes: Entropy changes during melting, boiling, sublimation
• Hess’s Law: Application of First Law to calculate enthalpy changes