Work and the First Law

First law of thermodynamics: conservation of internal energy under heat and work exchanges.

General idea of the topic

The first law is energy conservation applied to thermodynamic systems: what enters as heat and work accumulates as internal energy. This block builds that law from its three pieces: the system's internal energy, the work it exchanges with its surroundings, and the balance that ties them together.

What you will truly understand

• Why internal energy depends only on the system's state, while heat and work depend on the path taken.
• How to calculate the thermodynamic work of a gas from the area under the P-V curve.
• Why the first law (ΔU = Q − W) is simply energy conservation written with the thermodynamic sign convention.
• That no process, real or ideal, can violate this balance: it is the most basic restriction of all thermodynamics.

Recommended learning route

1. Internal Energy: the state quantity that the first law tracks.
2. Thermodynamic Work: how to calculate the work of an expanding or compressing gas.
3. First Law of Thermodynamics: the complete balance between heat, work, and internal energy.

Physical criterion you must acquire

First fix the sign convention you will use for heat and work, and keep it unchanged throughout the problem; most first-law errors come from mixing different conventions between the statement and the calculation.

Connection with real problems

The design of engines, compressors, and turbines, as well as any industrial energy balance, starts directly from applying the first law between the energy entering as heat and the energy leaving as useful work.

Final goal of the topic

Apply the first law with a consistent sign convention, calculate thermodynamic work in any process, and use internal energy as the control quantity of the energy balance.