Internal Energy: First Law, Work, and Heat
Internal energy (U) is a state function representing the total energy of a system. The first law of thermodynamics states ΔU = q + w: energy change equals heat transferred plus work done. For ideal gases, U depends only on temperature: ΔU = nCvΔT.
Why This Chemistry Calculation Matters
Why: Internal energy is fundamental to thermodynamics. The first law governs energy conservation. State functions like U are path-independent; heat and work are not. Understanding ΔU is essential for process analysis and calorimetry.
How: Use ΔU = q + w when heat and work are known. For ideal gases, ΔU = nCvΔT (Cv = 3R/2 monatomic, 5R/2 diatomic). Work at constant pressure: w = -PΔV. Sign convention: q > 0 heat in; w > 0 work on system.
- ●Internal energy is a state function—depends only on current state, not path.
- ●For ideal gases, isothermal processes have ΔU = 0 (U depends only on T).
- ●Adiabatic: q = 0, so ΔU = w; isochoric: w = 0, so ΔU = q.
Sample Examples
Calculation Mode
Process Type
Units
For educational and informational purposes only. Verify with a qualified professional.
🔬 Chemistry Facts
First law: ΔU = q + w (energy conservation).
— IUPAC
Work by system at constant P: w = -PΔV.
— NIST
Ideal gas: ΔU = nCvΔT; U independent of P and V.
— Kinetic theory
Isothermal ideal gas: ΔU = 0, so q = -w.
— Thermodynamics
📋 Key Takeaways
- • ΔU = q + w | First law: internal energy change from heat and work
- • ΔU = nCvΔT | Ideal gas: U depends only on temperature
- • w = -PΔV | Work at constant pressure
- • Isothermal: ΔU = 0 (ideal gas), q = -w
Did You Know?
Internal energy is a state function—path independent.
Source: Thermodynamics
For ideal gases, ΔU = 0 in isothermal processes.
Source: Kinetic theory
Adiabatic: q = 0, so ΔU = w (work only).
Source: First law
Isochoric: w = 0, so ΔU = q (heat only).
Source: Constant volume
Cv = (3/2)R monatomic, (5/2)R diatomic.
Source: Equipartition
Joule expansion: free expansion has ΔU = 0 for ideal gas.
Source: Joule experiment
How the Internal Energy Calculator Works
Enter heat (q) and work (w) for first law; or moles, Cv, and ΔT for ideal gas; or P, V₁, V₂ for work calculation.
First Law
ΔU = q + w — heat + work
Ideal Gas
ΔU = nCvΔT — U depends only on T
Expert Tips
Sign Conventions
q > 0: heat in; w > 0: work on system.
Cv Values
Monatomic: 12.5; diatomic: 20.8 J/(mol·K).
Process Type
Select isothermal, adiabatic, isochoric, or isobaric.
Units
Use J or kJ consistently; convert P to Pa.
Process Comparison
| Process | Constraint | ΔU |
|---|---|---|
| Isothermal | T constant | 0 (ideal gas) |
| Adiabatic | q = 0 | w |
| Isochoric | V constant | q |
| Isobaric | P constant | q + w |
Frequently Asked Questions
What is internal energy?
Total energy in a system: kinetic + potential of molecules. State function.
What is the first law?
ΔU = q + w. Energy change equals heat plus work.
Why ΔU = 0 for isothermal ideal gas?
U depends only on T for ideal gases; T constant ⇒ ΔU = 0.
What is w = -PΔV?
Work done BY system at constant P. Expansion (ΔV > 0) ⇒ w < 0.
When is heat capacity Cv used?
For constant-volume processes. ΔU = nCvΔT for ideal gas.
What is adiabatic?
No heat exchange (q = 0). All energy change from work.
How to find work from P-V?
w = -∫P dV. For constant P: w = -PΔV.
Key Numbers
📚 Official Sources
⚠️ Disclaimer: This calculator uses thermodynamic equations. For precise work, consult NIST Chemistry WebBook and IUPAC Gold Book.
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