2 Energy, Work, and Heat

Forms of energy

Energy can be transferred or converted from one form to another. For thermodynamic analysis, it is useful to distinguish energy associated with a system’s overall motion or position from energy within the system.

• Kinetic energy is associated with motion. A moving object has macroscopic kinetic energy, while molecules have microscopic kinetic energy from translation, rotation, and vibration.

• Potential energy is associated with position or interactions, including gravitational energy and the energy of interacting molecules.

• Chemical, electrical, and magnetic energy are associated with a system’s chemical composition or electrical and magnetic conditions.

A system’s total energy can include internal energy as well as its overall kinetic and potential energies. Which terms matter depends on the system and the process being studied.

Internal energy and system state

Internal energy, denoted by $U$, is associated with the microscopic motions and interactions of particles within a system. It includes microscopic kinetic energies and intermolecular potential energies, but not the energy of the system’s motion or position as a whole.

Internal energy is a state property: its value depends on the system’s state, not on how it reached that state. Consequently, the change in internal energy, $\Delta U$, between two states is determined by the initial and final states.

Heat and work across a boundary

Heat and work describe ways energy crosses the boundary between a system and its surroundings; they are not forms of energy stored in the system. The distinction is based on the transfer mechanism, not on what the energy becomes after it enters the system.

Heat transfer occurs because of a temperature difference, with energy flowing spontaneously from a higher-temperature region to a lower-temperature region. Work transfer occurs through an organized interaction other than transfer driven solely by a temperature difference. Examples include a force moving a piston, a rotating shaft turning a device, and electrical work done by a current.

Energy entering as heat may increase internal energy or contribute to expansion work. Work done on a system can also increase its internal energy. Once transferred, energy is accounted for as part of the system’s energy; it is not meaningful to say that the system contains heat or work.

The first law and energy bookkeeping

For a closed system, using the convention that heat added to the system is positive and work done by the system is positive, the first law is

where $Q$ is the net heat transferred into the system and $W$ is the net work done by the system. Heating a gas tends to raise its internal energy, while work done as the gas expands transfers energy out of it. Work done on the system has the opposite sign and tends to raise its energy.

For example, when gas in a cylinder is heated and pushes a movable piston outward, energy enters the gas by heat transfer and leaves it as work on the piston. The change in the gas’s internal energy depends on the net energy transfer, not on either transfer alone.

Heat and work are path-dependent transfers: their amounts depend on the process taken between states. By contrast, the change in internal energy depends only on the endpoints. Different processes can therefore deliver different amounts of heat and work while producing the same $\Delta U$.