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

🧮 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 m³

   • 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

🧠 State Functions vs. Path Functions

📝 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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