Heat was the missing piece that we needed to arrive at a completely general statement of the law of conservation of energy. Restating Equation 19.3, we have

Work and heat, two ways of transferring energy between a system and the environment, cause the system’s energy to change.

At this point in the text we are not interested in systems that have a macroscopic motion of the system as a whole. Moving macroscopic systems were important to us for many chapters, but now, as we investigate the thermal properties of a system, we would like the system as a whole to rest peacefully on the laboratory bench while we study it. So we will assume, throughout the remainder of Part V, that $\text{Δ}{E}_{\text{mech}}=0$.

With this assumption clearly stated, the law of conservation of energy becomes

The energy equation, in this form, is called the first law of thermodynamics or simply “the first law.” The first law is a very general statement about energy.

Chapters 9 and 10 introduced the basic energy model—basic because it included work but not heat. The first law of thermodynamics is the basis for a more general energy model, the thermodynamic energy model, in which work and heat are on an equal footing.

MODEL 19.1 Thermodynamic energy model

Thermal energy is a property of the system.

Full Alternative Text

• Work and heat are energies transferred between the system and the environment.

  • Work is energy transferred in a mechanical interaction.

  • Heat is energy transferred in a thermal interaction.

• The first law of thermodynamics says that transferring energy to the system changes the system’s thermal energy.

  • $\text{Δ}{E}_{\text{th}}=W+Q$

  • $W$ and $Q$ are positive when energy is added.

  • $W$ and $Q$ are negative when energy is removed.

• Limitations: Model fails if the system’s mechanical energy also changes.

Keep in mind that thermal energy isn’t the only thing that changes. Work or heat that changes the system’s thermal energy also changes other state variables, such as pressure, volume, or temperature. The first law tells us only about $\text{Δ}{E}_{\text{th}}$. Other laws and relationships, such as the ideal-gas law, are needed to learn how the other state variables change.