The first law of thermodynamics

• The internal energy of a system is the sum of the kinetic energy of its constituent particles and the potential energy associated with their configuration.
• For an ideal monatomic gas, internal energy reduces to the total translational kinetic energy of the atoms, because there are no interparticle forces and therefore no contributing potential energy.
• For an ideal gas, internal energy is directly proportional to absolute temperature, so doubling the absolute temperature doubles the internal energy.
• Changes to internal energy alter the microscopic (random) behavior of the particles without affecting the motion of the system's center of mass.

The First Law of Thermodynamics

The first law of thermodynamics is a statement of the conservation of energy applied to thermal systems.

Δ U = Q + W

Energy enters or leaves the system through heating (Q) and through work done (W) on or by the gas, and both terms must be applied with careful attention to their sign conventions.

W = -PΔ V

Sign conventions Q > 0 when heat is added to the system and Q < 0 when heat leaves it; W > 0 when work is done on the gas (compression, Δ V < 0) and W < 0 when the gas expands and does work on the surroundings.

• PV diagrams represent these processes graphically, with the area under the curve equal to the magnitude of the work done.
• Four special processes — isovolumetric (constant volume, so W = 0), isobaric (constant pressure, so W = -PΔ V), isothermal (constant temperature, so Δ U = 0 for an ideal gas), and adiabatic (no heat transfer, so Q = 0) — each hold one quantity fixed, eliminating a term from the first law and simplifying the analysis.
• Mastering the sign conventions and recognizing process types from the shapes of PV diagrams are the two most exam-critical skills in this topic.