What does ΔU = Q − W mean?

ΔU is the change in internal energy of the system. Q is the heat added to the system (positive when heat flows in). W is the work done by the system (positive when the system expands and does work on its surroundings). The equation states that the energy gained by a system equals heat added minus work the system performs.

What sign convention does this calculator use?

Standard physics sign convention: Q > 0 means heat flows into the system; W > 0 means the system does work on surroundings; ΔU > 0 means the internal energy increases.

What units should I use?

All values are in joules (J). For kilojoules, enter values in kJ and the result will also be in kJ — the equation is unit-consistent as long as all three use the same unit.

Does this apply to open systems?

The First Law in this form (ΔU = Q − W) applies to closed systems where no mass crosses the boundary. Open systems require additional enthalpy terms.

What if ΔU is negative?

A negative ΔU means the system lost internal energy — either more work was done by the system than heat added, or heat was removed from the system.

First Law of Thermodynamics Calculator

Name: First Law of Thermodynamics Calculator
Availability: InStock
Author: Nham Vu

Solve for heat (Q), work (W), or change in internal energy (ΔU) using ΔU = Q − W.

Solve for:

ΔU = Q − W · Enter heat added and work done by the system.

Q — Heat added (J)

W — Work done by system (J)

Sign Convention Reference

Variable	Positive (+)	Negative (−)
Q	Heat flows into the system	Heat flows out of the system
W	System does work on surroundings	Surroundings do work on system
ΔU	Internal energy increases	Internal energy decreases

Summary

Solve for heat (Q), work (W), or change in internal energy (ΔU) using ΔU = Q − W.

How it works

Select which variable you want to solve for: ΔU, Q, or W.
Enter the two known values in joules (J).
The calculator applies ΔU = Q − W and displays the result instantly.
Switch between solving for different variables without clearing your inputs.

Use cases

Check thermodynamics homework by solving for the unknown variable.
Verify heat transfer calculations in engineering design problems.
Explore how changes in heat or work affect internal energy.
Quickly compute ΔU for Carnot, Otto, or diesel cycle problems.

Frequently Asked Questions

Last updated: 2026-06-10 · Reviewed by Nham Vu