16. Thermodynamics

Internal energy U is the total microscopic kinetic and potential energy of a system. Its change depends only on initial and final states, not on the path.

Separate state variables from process quantities such as heat transfer and work, which depend on how the change occurs.

A gas can reach the same final temperature by slow compression or heating; its ∆U is the same if the initial and final states match.

Internal energy is not “heat contained” in an object, and work is not a state variable.

Raising temperature increases average microscopic kinetic energy, so internal energy generally rises; phase changes may instead change microscopic potential energy at constant temperature.

Identify whether energy enters as heating, work or both, and distinguish temperature change from state change.

Heating a solid raises its temperature until melting begins; during melting, energy continues to increase internal energy while temperature stays nearly constant.

Temperature is not a direct measure of total internal energy: mass, material and phase also matter.

For constant external pressure, work done by a gas during a volume change is W=p∆V, with expansion positive for work done by the gas under the chosen convention.

State the sign convention and distinguish work by the gas from work on the gas. For changing pressure, use the area under a p–V graph.

A gas expanding by 0.020 m³ against 1.0×10⁵ Pa does 2000 J of work.

The formula is not automatically valid when pressure changes significantly, and sign depends on the convention used.

The first law is ∆U=q+W when q is energy supplied as heat and W is work done on the system; equivalent conventions may write ∆U=Q−W_by.

Declare the sign convention before substituting. Internal energy rises when net energy enters and falls when net energy leaves.

If 300 J of heat enters and the system does 100 J of work, ∆U=200 J using the q−W_by convention.

The first law is energy conservation, not a statement that heat and work are stored properties of the system.