Find missing U, Q, or W using formulas. Convert units and compare process energy changes. Study first law behavior through practical worked examples here.
Enter any two core values. The tool solves the third one. Optional fields add cross checks.
| Case | Q | W | ΔU | Note |
|---|---|---|---|---|
| Heating with expansion | 120 kJ | 45 kJ | 75 kJ | Uses ΔU = Q − W |
| Cooling with compression | -35 kJ | -10 kJ | -25 kJ | System loses energy |
| Isochoric heating | 18 kJ | 0 kJ | 18 kJ | No boundary work |
| Known ΔU and Q | 90 kJ | 30 kJ | 60 kJ | Calculator solves W |
The main physics relation is the first law of thermodynamics.
Standard convention: ΔU = Q − W
Here, ΔU is the change in internal energy. Q is heat added to the system. W is work done by the system.
Alternate convention: ΔU = Q + W
This version is used when positive work means work done on the system.
Temperature method: ΔU = nCvΔT
This helps estimate internal energy change for many closed system problems.
Constant pressure work: W = P(V2 − V1)
Use consistent units before comparing values.
Step 1. Enter a process name for your record.
Step 2. Choose the work sign convention used by your textbook or class.
Step 3. Enter any two of ΔU, Q, and W with their units.
Step 4. Choose the output unit you want for the final answer.
Step 5. Add optional n, Cv, and temperatures for a thermal cross check.
Step 6. Add pressure and two volumes for a constant pressure work check.
Step 7. Press calculate. The result appears above the form.
Step 8. Download the result as CSV or PDF when needed.
The U Q W calculator helps students solve first law problems with less confusion. It focuses on internal energy, heat transfer, and boundary work. These terms appear in many physics lessons, engineering examples, and lab activities. A clean calculator reduces sign mistakes. It also speeds up routine checks. This is useful during revision, classroom practice, and homework review. A clear layout lets users see the relation between energy gained, energy lost, and work interaction in one place.
U represents the change in internal energy of a system. Q represents heat transferred into or out of the system. W represents work linked with expansion, compression, or another process. Together, these values describe how energy moves during a thermodynamic change. This relation is central in physics. It is also important in chemistry and mechanical engineering. Once users understand the sign convention, they can solve closed system examples with greater confidence and fewer algebra errors.
This calculator solves any missing variable when two core values are known. It also converts units automatically. That helps when one value is given in kilojoules, calories, watt hours, or joules. The optional temperature section estimates internal energy change through nCvΔT. The constant pressure section estimates PV work. These added checks improve confidence. They also help compare a direct first law result with a model based estimate from thermal properties or simple piston cylinder data.
Use this page for isochoric, isobaric, heating, cooling, compression, and expansion cases. It is helpful for homework review. It is also useful before quizzes and lab sessions. Teachers can use it for worked examples in class. Learners can use it to verify hand calculations after solving a problem manually. Since the result appears above the form, users can review the answer quickly, compare values, and adjust inputs without losing track of the current calculation.
The result section shows solved values, residual balance, and optional comparison outputs. This supports better interpretation. A near zero balance confirms consistency with the chosen equation. The CSV option helps save records. The PDF option helps share results. Output tables also support neat documentation. Overall, this U Q W calculator turns a common energy equation into a practical study tool. It helps users test sign choices, compare methods, and understand the physical meaning of each thermodynamic process.
U means the change in internal energy. Many books write it as ΔU. It measures how the system energy changes during heating, cooling, compression, or expansion.
Different books use different work conventions. Some treat work by the system as positive. Others treat work on the system as positive. This calculator lets you choose either method.
Enter any two of the three main quantities. The calculator then solves the missing one. Optional temperature and PV fields are only for cross checking.
Yes. Each main energy input has its own unit selector. The calculator converts everything internally before solving and then shows the result in your chosen output unit.
W is zero in many constant volume cases. If the volume does not change, boundary work is often zero. Then the heat transfer equals the internal energy change.
It gives an estimate of internal energy change for many closed system models. It is especially useful when the amount of substance, heat capacity, and temperature change are known.
The residual shows whether the entered or solved values satisfy the selected first law equation. A result near zero means the energy relation is consistent.
Yes. Use the CSV button for spreadsheet style storage. Use the PDF button for a shareable page export. The print option is also included.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.