Energy, Work & the First Law Explained | Chapter 19 of University Physics

Chapter 19 establishes how heat and work transfer energy into and out of a system and unifies them through the First Law of Thermodynamics. You’ll learn how to track internal energy changes, interpret p–V diagrams, and distinguish the major thermodynamic processes that govern ideal gases.

Watch the full video summary here for detailed explanations and examples.

Thermodynamic Systems & Processes

A thermodynamic system is the specific collection of matter under study, while the surroundings encompass everything else. A thermodynamic process describes how the system’s state variables—temperature (T), pressure (p), volume (V), and internal energy (U)—change when heat or work crosses the boundary.

Heat & Work

Heat (Q) is energy transferred due to temperature difference: positive when entering the system, negative when leaving. Work (W) is energy transfer via macroscopic forces: positive when done by the system on the surroundings (expansion), negative when done on the system (compression). For volume work,

W = ∫ p dV (the area under the p–V curve).

The First Law of Thermodynamics

The First Law links heat, work, and internal energy, treating U as a state function:

ΔU = Q – W

In differential form: dU = dQ – p dV. This expression shows that internal energy change depends only on the initial and final states, not the specific path.

Key Thermodynamic Processes

• Adiabatic (Q = 0): ΔU = –W
• Isochoric (V = constant): W = 0 → ΔU = Q
• Isobaric (p = constant): W = p ΔV → ΔU = Q – p ΔV
• Isothermal (T = constant, ideal gas): ΔU = 0 → Q = W

Internal Energy & Heat Capacities of Ideal Gases

For an ideal gas, internal energy depends solely on temperature: ΔU = n C_V ΔT. Heat added at constant volume: Q = n C_V ΔT. At constant pressure: Q = n C_P ΔT,

with C_P = C_V + R and ratio γ = C_P/C_V.

Adiabatic Process Equations

During a reversible adiabatic change in an ideal gas:

• p V^γ = constant
• T V^γ–1 = constant
• Work done: W = (1/(γ–1)) (p₁V₁ – p₂V₂) = n C_V (T₁ – T₂)

Conclusion

Chapter 19 shows that energy conservation in thermodynamics extends beyond mechanics: heat and work are interchangeable forms of energy transfer, governed by ΔU = Q – W. By mastering the key processes—adiabatic, isochoric, isobaric, and isothermal—and their equations, you can analyze any ideal-gas cycle with confidence.

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