Library / Thermodynamics / THE-10
Thermodynamics
First law of thermodynamics
Change in internal energy equals heat added to the system minus work done by the system.
- Ref
- THE-10
- Rev
- v1
- Field
- Thermodynamics
- Result
- ΔU [J]
Q is the heat added to the system and W the work done by the system on its surroundings, both in joules. ΔU is the change in internal energy, which for a gas shows as a change in temperature. This is the physics sign convention: heat in is positive and work out is positive. Chemistry texts often write ΔU = Q + W, with W as work done on the system.
Change in internal energy equals heat added to the system minus work done by the system.
Calculator
- Share of the heat converted to work40 %
- Work for no change in internal energy (ΔU = 0)500 J
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- The defaults add 500 J of heat and let 200 J leave as work, so 300 J stays in the gas and its temperature rises.
- If all the heat leaves as work (W = Q), ΔU = 0 and the temperature stays put, as in a slow isothermal expansion.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (J) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Q Heat added | −10,000 to 10,000 J | −10,200 | 9,800 | 20,000 | +400 J | +133 % |
| W Work done by the system | −10,000 to 10,000 J | −9,500 | 10,500 | 20,000 | +400 J | −133 % |
Sweep of Heat added
| Heat added (J) | Change in internal energy (J) |
|---|---|
| −10,000 | −10,200 |
| −7,500 | −7,700 |
| −5,000 | −5,200 |
| −2,500 | −2,700 |
| 0 | −200 |
| 2,500 | 2,300 |
| 5,000 | 4,800 |
| 7,500 | 7,300 |
| 10,000 | 9,800 |
Sweep one variable
Variables and how each one contributes
Change in internal energy
What the equation gives you. Everything else feeds it.
Heat added
Heat added to the system (negative if heat flows out). Raises ΔU one-for-one: an extra joule of heat is an extra joule of internal energy, if the work is unchanged.
Work done by the system
Work done by the system on its surroundings (negative if work is done on it). Lowers ΔU one-for-one: energy sent out as work is no longer available to heat the gas.
Worked example with the values above
- Heat in: Q = 500 J. Work out: W = 200 J.
- Subtract: Q − W = 500 − 200.
- ΔU = 300 J, so the internal energy rises.
Assumptions and limits
- A closed system with no flow of mass across the boundary.
- Changes in the bulk kinetic and potential energy of the system are negligible.
Common mistakes
- Using the wrong sign convention: check whether W is defined as work done by the system or on it.
- Using it for an open system such as a turbine or nozzle, which also needs flow work (see the steady-flow energy equation).
Statistics and uncertainty
ΔU is a difference, so the relative error grows when Q and W are close. With 5 % errors on Q = 500 J and W = 200 J the error on ΔU is about ±27 J (9 %). If they were 500 and 480, the same percentage errors would give ±35 J on a ΔU of only 20 J.
Where it is used
- Energy accounting for engines, compressors and sealed vessels.
- Checking that heat and work measurements from a test agree.
Maths you need
- Conservation of energy: energy is neither created nor destroyed
- Signs: heat in and work out are positive