When heat is supplied to an object, its internal energy increases, it does work on the outside, or both occur. The first law of thermodynamics formulates this relationship.
Basic Knowledge
Internal energy U (the thermodynamic U here): The sum of the kinetic and potential energies of the molecules making up an object. It increases or decreases in proportion to temperature.
First law of thermodynamics:ΔU = Q + W
ΔU: change in internal energy (J)
Q: heat absorbed by the object (J) (positive when absorbed, negative when released)
W: work done on the object by the outside (J) (positive when compressed, negative when expanded)
In words: “Change in internal energy = absorbed heat + work done on the object from outside”
The notation may differ among textbooks. If W' means work done by the object, then W = -W'.
This is the thermodynamic expression of the law of conservation of energy.
Internal energy U（The sum of the kinetic energy and other energies of molecules inside an object. Proportional to temperature）
First law of thermodynamics（ΔU = Q + W. The thermodynamic version of energy conservation）
Heat absorption and heat release（Q>0 when heat is absorbed, Q<0 when heat is released）
Adiabatic change（A change with Q = 0. ΔU = W only）
Isothermal change（ΔU = 0. A gas expands or is compressed at constant temperature）
Constant-volume change（Constant volume. Work done on the outside W' = 0. ΔU = Q）
Further Study (Background and Significance)
The first law of thermodynamics is “the thermodynamic version of the law of conservation of energy.” It shows that heat and work are both forms of energy and can be converted into each other. James Prescott Joule (J.P. Joule, 1843) first clearly established this relationship and experimentally determined the mechanical equivalent of heat (1 cal ≈ 4.2 J).
In an adiabatic change (Q=0), only ΔU = W applies. When work compresses an object from outside, its internal energy and temperature increase. During expansion, its temperature decreases. This principle is used in diesel engines, which ignite diesel fuel through adiabatic compression alone.
In an isothermal change (ΔU = 0), Q = -W. When a gas expands isothermally, it absorbs heat and does work on the outside.
A refrigerator is a device based on the first law of thermodynamics; it uses electrical energy (work) to move heat from inside the refrigerator to the outside.
- ΔU = Q + W (Q: heat absorption, W: work done on the object from outside)
- Internal energy = sum of the kinetic energies of molecules
- Temperature ↑ → internal energy ↑
- Adiabatic change: Q=0 → ΔU = W
- Isothermal change: ΔU=0 → Q = -W
- Constant-volume change: W=0 → ΔU = Q
- Heat and work are both forms of energy
Important Notes (Common Confusions)
① Pay attention to the sign convention for W. If W is defined as “work done on the object from outside,” ΔU = Q + W. If W' is defined as “work done by the object,” ΔU = Q - W'. The definition differs among textbooks. ② “Adiabatic” means no heat transfer (Q=0), not “constant temperature (isothermal).” Temperature can change during an adiabatic change. ③ The change in internal energy ΔU can be determined from the temperature change. If temperature rises, ΔU > 0. ④ The first law of thermodynamics applies not only to gases but also to solids and liquids.
Practice
- A gas received 500 J of heat, and 200 J of work was simultaneously done on it from outside. Find the change in internal energy.
- In an adiabatic change, a gas did 300 J of work on the outside. How did its internal energy change?
- In an isothermal change, a gas absorbed 400 J of heat. How much work did the gas do on the outside?