Topic 8.1.16 min read
Internal Energy
Internal energy is the sum of the microscopic kinetic and potential energies of a system. It is a state function, so its change depends only on the initial and final states, not the path between them.
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Beginner Level
Molecules move and interact even when an object looks still. The total microscopic motion and interaction energy inside the object is its internal energy.
Recommended for Class 11
Internal Energy
Overview
Internal energy is the sum of the microscopic kinetic and potential energies of a system. It is a state function, so its change depends only on the initial and final states, not the path between them.
Learning Outcomes
- Internal energy includes molecular kinetic and potential energies.
- For an ideal gas, internal energy depends on temperature.
- Average translational kinetic energy is 3kT/2.
- Heating and mechanical work can increase internal energy.
- ΔU = U₂ − U₁.
- Internal energy is a state function.
Intermediate Level
Definition
Internal energy U is the sum of all molecular forms of energy, especially random kinetic energy and intermolecular potential energy.
Ideal Gas
In the ideal-gas model, particles have negligible volume, no intermolecular attraction away from collisions and perfectly elastic collisions. Its internal energy is associated with molecular motion.
Raising absolute temperature increases average molecular kinetic energy and therefore the internal energy of an ideal gas.
Ways to Change Internal Energy
- Heating transfers energy into molecular motion or bonding energy.
- Mechanical work such as rubbing or hammering can increase random molecular energy.
- Friction converts macroscopic mechanical energy into internal energy.
State Function
If a system moves from state A to state B by different paths on a PV diagram, ΔU is the same for every path. Only the endpoint states matter.
| Change | Relation | Sign of ΔU |
|---|---|---|
| temperature rises | U₂ > U₁ | positive |
| temperature falls | U₂ < U₁ | negative |
| ideal-gas temperature unchanged | U₂ = U₁ | zero |
Real Gas
Real gas molecules attract one another, so internal energy includes both kinetic and intermolecular potential energy and can depend on temperature and volume.
Average Molecular Energy
Find average translational kinetic energy at 298 K using k = 1.38 × 10⁻²³ J K⁻¹.
- T = 298 K
〈K〉 = 3kT/2
〈K〉 = (32)(1.38 × 10⁻²³)(298)
Final answer: 〈K〉 = 6.17 × 10⁻²¹ J
Common Mistakes
- Use kelvin in gas and molecular-energy equations.
- Distinguish heat, temperature and internal energy.
- Convert all quantities to SI units before calculation.
Short-Question Preparation
Q. Define internal energy.
A. The sum of microscopic kinetic and potential energies of a system.
Q. Why is U a state function?
A. Its change depends only on the initial and final states, not the process path.
Q. How can U increase?
A. By heating the system or doing mechanical work on it.
Q. State the sign convention.
A. ΔU = U₂ − U₁; it is positive for an increase and negative for a decrease.
Sticky Notes
- Internal energy includes molecular kinetic and potential energies.
- For an ideal gas, internal energy depends on temperature.
- Average translational kinetic energy is 3kT/2.
- Heating and mechanical work can increase internal energy.
- ΔU = U₂ − U₁.
- Internal energy is a state function.
60-Second Revision
Internal energy is the sum of the microscopic kinetic and potential energies of a system. It is a state function, so its change depends only on the initial and final states, not the path between them.
Summary
Internal energy is the sum of the microscopic kinetic and potential energies of a system. It is a state function, so its change depends only on the initial and final states, not the path between them.
Ask-the-Tutor Modes
- Explain it simply.
- Compare the key terms.
- Solve a numerical.
- Prepare a board-style answer.
- Test me with an MCQ.
Exam Focus
Exam Focus
Important points
- Internal energy includes molecular kinetic and potential energies.
- For an ideal gas, internal energy depends on temperature.
- Average translational kinetic energy is 3kT/2.
- Heating and mechanical work can increase internal energy.
- ΔU = U₂ − U₁.
- Internal energy is a state function.
Common exam traps
- Wrong temperature scale
Long question structure
Definition → explanation → equations → examples.
Common Mistakes
Common Mistakes
- Mistake
Keep heat, temperature and internal energy distinct.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
Internal energy includes molecular kinetic and potential energies.
For an ideal gas, internal energy depends on temperature.
Average translational kinetic energy is 3kT/2.
Heating and mechanical work can increase internal energy.
Internal energy is the sum of the microscopic kinetic and potential energies of a system. It is a state function, so its change depends only on the initial and final states, not the path between them.
- Definition
- Internal energy is the sum of the microscopic kinetic and potential energies of a system. It is a state function, so its change depends only on the initial and final states, not the path between them.
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Exam Practice
Important Question
Q1. Define internal energy.
Important Question
Q2. Why is U a state function?
Important Question
Q3. How can U increase?
Important Question
Q4. State the sign convention.