First Law: ΔU = Q − W | Calculate Heat, Work & Internal Energy Change
Result
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📝 Step-by-step solution
Select what to calculate and enter values
💡 ΔU = Change in internal energy (J) | Q = Heat added (J) | W = Work done by system (J) | 1 J = 1 N·m
📖 What is the First Law of Thermodynamics?
The First Law of Thermodynamics is a statement of energy conservation: energy can be
transferred or converted, but it cannot be created or destroyed. It is often called the Law of
Conservation of Energy. For a closed system, the change in internal energy (ΔU) equals the
heat added (Q) minus the work done by the system (W):
ΔU = Q − W
Where:
• ΔU = Change in internal energy (Joules)
• Q = Heat added to the system (Joules)
• W = Work done by the system (Joules)
🔁 Rearranged Formulas
Internal Energy: ΔU = Q − W Heat: Q = ΔU + W Work: W = Q − ΔU
📝 Worked Example
Example: Gas Absorbs 500 J of Heat and Does 200 J of Work
Given: Q = 500 J (heat added) | W = 200 J (work done by gas)
Formula: ΔU = Q − W Calculation: ΔU = 500 − 200 = 300 J Result: The internal energy of the gas increases by 300 J.
🔬 Sign Conventions (Very Important)
Q is positive (+) → heat added to system Q is negative (−) → heat removed from system
W is positive (+) → work done by system (expansion) W is negative (−) → work done on system (compression)
ΔU is positive (+) → internal energy increases ΔU is negative (−) → internal energy decreases
📊 Common Thermodynamic Processes
Isothermal: ΔT = 0 → ΔU = 0 → Q = W
Adiabatic: Q = 0 → ΔU = −W
Isochoric (constant volume): W = 0 → ΔU = Q
Isobaric (constant pressure): W = P × ΔV
⚠️ Limitations & Assumptions
📌 Important Notes
Assumes a closed system — no mass enters or leaves.
Uses standard physics sign convention: W is work done by the system.
Some engineering textbooks use the opposite convention (ΔU = Q + W) — always check.
Does not account for kinetic or potential energy changes (only internal energy).
Results are theoretical — real systems may have heat losses to surroundings.
📚 Sources & References
Authoritative Sources
OpenStax — University Physics, Volume 2: Thermodynamics
NIST — Thermodynamic Data & Standards
Khan Academy — First Law of Thermodynamics
Serway & Jewett — Physics for Scientists and Engineers
MIT OpenCourseWare — Thermodynamics & Kinetics
❓ Frequently Asked Questions
What is internal energy?
Internal energy (U) is the total kinetic and potential energy of all the particles
inside a system. It includes molecular motion, vibrations, and intermolecular forces. We can only
measure changes in internal energy (ΔU), not absolute values.
Why is work done "by" the system positive?
In the standard physics convention, work done by the system (e.g., gas expanding and pushing
a piston) removes energy from the system, so it is subtracted from heat in the formula ΔU = Q − W.
This is the most common convention in physics textbooks.
What is an adiabatic process?
An adiabatic process is one where no heat is exchanged with the surroundings (Q = 0).
In this case, ΔU = −W. If a gas expands adiabatically, it does work and its internal energy (and temperature)
drops, which is why compressed air cans get cold when you release them.
Can internal energy change without heat or work?
No. For a closed system, the internal energy can only change through heat transfer or work.
If both Q = 0 and W = 0, then ΔU = 0 (internal energy is constant).
This Thermodynamics Calculator is provided for informational and educational purposes only.
Results are based on the standard First Law of Thermodynamics (ΔU = Q − W) with the physics sign
convention. Some textbooks and engineering disciplines use different sign conventions — always
verify with your course material or a qualified instructor. Real systems may deviate due to
heat losses, friction, and non-ideal behavior.