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.
Key equation
\langle K\rangle=32kT
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.
Key equation
Δ U=U2-U1
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.
1
Given
T = 298 K
2
Working
〈K〉 = 3kT/2
3
Step 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.
Did you understand this topic?
Your answer is saved with your learning record. It does not mark the topic as mastered.
Exam preparation
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 mistakes
Keep heat, temperature and internal energy distinct.
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.
Internal Energy
Sticky Notes · Quick Revision
1.
Key Point 1
Internal energy includes molecular kinetic and potential energies.
2.
Key Point 2
For an ideal gas, internal energy depends on temperature.
3.
Key Point 3
Average translational kinetic energy is 3kT/2.
4.
Key Point 4
Heating and mechanical work can increase internal energy.
