Calculator
Use consistent signs for heat and work. Positive heat adds energy to the system. Choose the work convention that matches your course or lab notes.
Formula used
The first law relates internal energy change to heat and work. Using a common sign convention: ΔU = Q − W, where W is the work done by the system.
If your convention defines W as work done on the system, the calculator applies: ΔU = Q + W. Units are converted internally, then returned to your selected unit.
How to use this calculator
- Choose the quantity you want to compute: Q, W, or ΔU.
- Select the sign convention that matches your notes.
- Pick a single energy unit for all entered values.
- Enter the two known values, leaving the unknown blank.
- Press Calculate to show results above the form.
- Use the download buttons to export CSV or PDF.
Example data table
| Case | Convention | Q (kJ) | W (kJ) | ΔU (kJ) | Notes |
|---|---|---|---|---|---|
| 1 | By system | 2.5 | 0.8 | 1.7 | Heat in, system does work. |
| 2 | By system | 1.2 | -0.4 | 1.6 | Negative W means work done on system. |
| 3 | On system | 3.0 | 0.6 | 3.6 | Work on system increases internal energy. |
Tip: If you see a sign mismatch, switch conventions or revisit how W was defined in your problem statement.
Energy accounting in closed systems
The first law is an energy balance for a closed system. This calculator links internal energy change ΔU to heat transfer Q and work W after you choose a sign convention. It fits pistons, rigid tanks, and calorimetry cases where mass stays within the boundary.
Choosing a sign convention that matches your course
Many texts use ΔU = Q − W when W is work done by the system. Others use ΔU = Q + W when W is work done on the system. Mixing these rules is the fastest way to get incorrect signs, so pick one and stay consistent.
Typical magnitudes and units you may encounter
Thermal labs often report kJ, while chemistry may use calories or kilocalories. As a reference, a 100 W heater running for 5 minutes delivers about 30 kJ of energy. Gas expansion work can be comparable during large volume changes.
Interpreting positive and negative results
Positive ΔU means the system stored energy internally. Negative ΔU means net energy left. Under the “by system” convention, positive W indicates the system did work on surroundings, which tends to reduce ΔU unless compensated by positive Q. In engines and compressors, work terms may exceed heat briefly, causing ΔU to drop unexpectedly quickly during expansion.
Solving for the unknown in practical workflows
Use “Solve for” to compute ΔU from measured Q and W, infer Q from a measured state change and work term, or back-calculate W when heating and ΔU are known. This mirrors lab reporting where two quantities are measured and the third is derived.
Data checks before exporting
Run quick checks: if a rigid container does negligible boundary work, W should be near zero and ΔU should track Q. If Q and W have similar magnitudes and signs, ΔU should be relatively small. Over a complete cycle, net ΔU should be near zero.
Worked-data example you can replicate
If Q = 2.5 kJ and W = 0.8 kJ (by-system convention), then ΔU = 1.7 kJ. Switch to the “on system” convention to match problems that define W in the opposite direction; the calculator updates the equation and result accordingly.
Why exports support reports and audits
CSV suits spreadsheets and multi-trial logs, while PDF is convenient for attachments and printouts. Exports include Q, W, ΔU, the chosen convention, and the equation used, so a reviewer can reproduce the calculation without guessing your sign rules.
FAQs
What does ΔU represent in this calculator?
ΔU is the change in internal energy between two states. It includes temperature changes, phase changes, and microscopic energy storage effects within the system boundary.
Can I enter negative values for Q or W?
Yes. Negative Q means heat leaves the system. The meaning of W depends on the selected convention, so choose it first and keep your signs consistent with that definition.
Which units can I use?
You can use joules, kilojoules, calories, kilocalories, and BTU. Enter all values in the same unit, and the calculator converts internally for consistent computation.
Why does changing the convention change the answer?
Because the sign attached to work differs across textbooks. When W is defined in the opposite direction, the equation changes from ΔU = Q − W to ΔU = Q + W.
What if my system does negligible boundary work?
Set W to 0 (or a small estimate). In a rigid container, this is common, and the first law reduces to ΔU ≈ Q under consistent sign usage.
How accurate are the exports?
CSV and PDF exports are generated from the same inputs and equation used on screen. They include the convention and equation so results can be reproduced in audits.
Is this calculator suitable for open systems?
It is intended for closed-system energy balances using Q, W, and ΔU. For open systems with flow work and enthalpy, you would typically use steady-flow energy equations instead.