First Law of Thermodynamics Calculator
The change in internal energy from the heat going in and the work coming out, with the temperature change it implies.
Results
What this tool does
The first law is energy conservation written for systems that get hot. Whatever heat you put in either stays inside as internal energy or leaves as work done on the surroundings — nothing else is available to it. That single sentence, ΔU = Q − W, is the foundation the whole of thermodynamics is built on, and it is also the reason perpetual motion machines cannot work. Put in the heat and the work, watch the balance, and if you give a mass and a specific heat the page also converts the leftover energy into the temperature rise it produces.
Formula
ΔU = Q − W · Q > 0 when heat goes in, W > 0 when the system does work
Variables
| Symbol | Meaning | Unit |
|---|---|---|
q | Heat put into the system | J |
w | Work done by the system | J |
m | Mass | kg |
c | Specific heat capacity | J/(kg·K) |
DU | Change in internal energy | J |
DT | Temperature change | K |
QK | Energy in kilojoules | kJ |
WK | Work in kilojoules | kJ |
UK | Internal energy change in kilojoules | kJ |
PR | What happens to the system | — |
Worked example
- Heat put into the system5000 J
- Work done by the system2000 J
- Mass1 kg
- Specific heat capacity718 J/(kg·K)
- Change in internal energy3000.0000 J
- Temperature change4.178273 K
- Energy in kilojoules5.0000 kJ
- Work in kilojoules2.0000 kJ
- Internal energy change in kilojoules3.0000 kJ
- What happens to the systemIt gains internal energy
Limitations
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
Frequently asked questions
Which way round are the signs?
Heat added to the system is positive; work done by the system on its surroundings is positive. So a gas that is heated and pushes a piston out has a positive Q and a positive W, and the internal energy rises only by whatever is left over. Some engineering texts flip the work sign and write ΔU = Q + W, meaning work done on the system — both are correct and both are in print, so check which one a book is using before comparing answers. To enter a system being compressed here, give the work as a negative number.
Why can the internal energy fall while heat is going in?
Because the system can be doing more work than it is receiving in heat, and the difference has to come from somewhere. A gas expanding against a piston while being only gently warmed cools down, which is exactly how a refrigerant behaves passing through an expansion valve. The first law does not say energy cannot leave — it says it has to be accounted for. Everything that goes in as heat either stays as internal energy or leaves as work, with nothing unexplained on either side.