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5.4

🧪 Chapter 5.4 Study Guide: The First Law of Thermodynamics


🔥 GOALS of Section 5.4

  • Understand how heat (q) and work (w) affect a system's internal energy (ΔU).

  • Calculate P–V work done during gas expansion or compression.

  • Determine changes in enthalpy (ΔH) and internal energy (ΔU).

  • Identify and explain state functions (values determined only by the system’s state).


Core Concepts & Definitions

Term

Definition

Thermodynamics

Study of energy, heat, and work in systems.

System

The part of the universe under study (e.g., gas in a cylinder).

Surroundings

Everything else that can exchange energy with the system.

Heat (q)

Energy transferred due to temperature difference.

Work (w)

Energy transferred when a force moves an object (e.g., gas expansion).

Internal Energy (U)

Sum of potential and kinetic energies of particles in a system.

Enthalpy (H)

Heat content of a system at constant pressure: H=U+PVH = U + PVH=U+PV.

State Function

Depends only on the system’s state, not the path taken (e.g., ΔU, ΔH).

Path Function

Depends on the process/path taken (e.g., q, w).


🧮 Key Equations

  1. First Law of Thermodynamics

    ΔU=q+w\Delta U = q + wΔU=q+w

    • q>0q > 0q>0: heat into the system (endothermic)

    • w>0w > 0w>0: work done on the system

    • q<0q < 0q<0: heat out of the system (exothermic)

    • w<0w < 0w<0: work done by the system

  2. P–V Work (Gas Expansion/Compression)

    w=−PΔVw = -P \Delta Vw=−PΔV

    • PPP in Pascals (Pa)

    • ΔV\Delta VΔV in

    • Note: Convert L to m³ → 1 L=0.001 m31 \text{ L} = 0.001 \text{ m}^31 L=0.001 m3

  3. Enthalpy Change at Constant Pressure

    ΔH=ΔU+PΔV=qp\Delta H = \Delta U + P\Delta V = q_pΔH=ΔU+PΔV=qp​

    • ΔH>0\Delta H > 0ΔH>0: endothermic

    • ΔH<0\Delta H < 0ΔH<0: exothermic


📊 Sign Conventions

Type of Transfer

Sign of q or w

Effect on Internal Energy (ΔU)

Heat into system

q>0q > 0q>0

ΔU>0\Delta U > 0ΔU>0

Heat out of system

q<0q < 0q<0

ΔU<0\Delta U < 0ΔU<0

Work on system

w>0w > 0w>0

ΔU>0\Delta U > 0ΔU>0

Work by system

w<0w < 0w<0

ΔU<0\Delta U < 0ΔU<0


🧠 State Functions vs. Path Functions

State Function (depends only on initial & final states)

Path Function (depends on route taken)

Internal energy (U)

Heat (q)

Enthalpy (H)

Work (w)

Temperature (T), Pressure (P), Volume (V)

📝 Example: Heating a substance from 25°C to 75°C:

  • ΔT = 50°C no matter how you got there → state function.

  • The heat or work involved may differ → path function.


🔍 Examples to Know

🔸 Example 1: Sublimation of CO₂
  • CO₂(s) → CO₂(g)

  • Heat is absorbed → q>0q > 0q>0

  • Work is done by the gas → w<0w < 0w<0

  • Use:

    ΔU=q+w\Delta U = q + wΔU=q+w

🔸 Example 2: Constant Volume Process
  • ΔV=0⇒w=0\Delta V = 0 \Rightarrow w = 0ΔV=0⇒w=0

  • Then ΔU=qv\Delta U = q_vΔU=qv​

🔸 Example 3: Constant Pressure Process
  • If only P–V work:

    ΔH=qp\Delta H = q_pΔH=qp​


🧩 Common Test Questions

Define internal energy and describe how it changes.
Use ΔU=q+w\Delta U = q + wΔU=q+w to solve word problems.
Calculate work done by or on a gas using w=−PΔVw = -P\Delta Vw=−PΔV.
Identify if a quantity is a state function or not.
Determine if a process is exothermic or endothermic based on sign of qqq or ΔH\Delta HΔH.
Explain why ΔH=qp\Delta H = q_pΔH=qp​ under constant pressure.


📚 Study Tips

  • Memorize sign conventions.

  • Practice problems calculating qqq, www, ΔU\Delta UΔU, and ΔH\Delta HΔH.

  • Understand examples involving gas expansion, sublimation, or constant volume.

  • Compare state and path functions with real-world analogies (like altitude vs. distance).


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