Heat, Engines & Entropy Explained | Chapter 20 of University Physics

Chapter 20 introduces the Second Law of Thermodynamics and explores how it determines the direction of natural processes. You’ll learn the difference between reversible and irreversible processes, how heat engines and refrigerators operate, and why entropy—a measure of disorder—always increases in real systems.

Watch the full video summary here for step-by-step explanations and examples.

Reversible vs Irreversible Processes

Reversible processes are ideal, quasi-static, and maintain equilibrium at each step. In contrast, irreversible processes—such as spontaneous heat flow, friction, and free expansion—occur in one direction and generate entropy. Real-world systems are inherently irreversible, highlighting the fundamental “arrow of time.”

Heat Engines

Heat engines convert thermal energy into mechanical work by absorbing heat Q_H from a hot reservoir, doing work W, and releasing residual heat Q_C to a cold reservoir. Their efficiency is:

e = W / Q_H = 1 – (Q_C / Q_H)

The First Law for a cyclic process gives Q_H = W + Q_C, ensuring energy balance.

Internal Combustion Engines (Otto Cycle)

The Otto cycle models a four-stroke engine: intake, adiabatic compression, adiabatic power (ignition), and exhaust. Efficiency depends on the compression ratio r and the heat-capacity ratio γ = C_P/C_V:

e_Otto = 1 – 1 / r^(γ – 1)

Refrigerators & Heat Pumps

Refrigerators reverse the engine cycle, using work to move heat from a cold to a hot reservoir. Their coefficient of performance is:

K = Q_C / W = Q_C / (Q_H – Q_C)

A higher K indicates more effective cooling per unit work.

Second Law of Thermodynamics

The Second Law has two equivalent statements:

• Heat cannot flow spontaneously from cold to hot without work input.
• No cyclic process can convert all heat into work.

These principles enforce irreversibility and set limits on engine and refrigerator performance.

Carnot Cycle & Maximum Efficiency

The Carnot cycle is an ideal reversible engine comprising two isothermal and two adiabatic processes. Its maximum efficiency is:

e_Carnot = 1 – (T_C / T_H) (temperatures in Kelvin)

The corresponding refrigerator performance is K_Carnot = T_C / (T_H – T_C). No real engine can surpass these limits.

Kelvin Scale & Absolute Zero

The Kelvin temperature scale is defined via Carnot cycle ratios, making it substance-independent. Absolute zero (0 K) is the theoretical lower limit where molecular motion ceases.

Entropy & Statistical Interpretation

Entropy (S) quantifies disorder. For a reversible heat exchange:

dS = dQ / T, and over a cycle ∮dQ/T = 0. In any real (irreversible) process, total entropy increases:

ΔS_total ≥ 0

Statistically, S = k ln w, where k is Boltzmann’s constant and w the number of microscopic states. Systems evolve toward macrostates with more microstates—higher entropy.

Conclusion

Chapter 20 demonstrates that while energy is conserved, its utility diminishes due to irreversibility and entropy production. Heat engines and refrigerators operate within the bounds set by the Second Law and Carnot efficiency, and entropy provides a unifying measure of irreversibility and disorder.

For detailed examples and derivations, watch the full video summary here. Keep exploring more chapters on Last Minute Lecture to deepen your thermodynamics expertise.

If you found this breakdown helpful, be sure to subscribe to Last Minute Lecture for more chapter-by-chapter textbook summaries and academic study guides.