Chapter 2: First Law of Thermodynamics

The law posits that energy can be converted between forms and introduces the concept that the transfer of thermal energy, or heat (q), is a quality of energy distinct from energy transferred as work (w). Historically, this relationship was quantified through the pioneering experiments of Count Rumford and James Prescott Joule, which defined the mechanical equivalent of heat and established the calorie as the standard unit of thermal energy. A fundamental principle of the First Law is that while the transfer of heat and work are path-dependent processes that occur on or to a system, the resulting change in internal energy (U) is path-independent, meaning it relies only on the initial and final states. The First Law is summarized by the relationship that the change in the system's internal energy equals the heat absorbed by the system minus the work performed by the system. To analyze specific processes, the text examines paths such as constant volume (isochoric) processes, where work is zero, meaning the change in internal energy equals the heat absorbed at constant volume. For constant pressure (isobaric) processes, a second major state function, enthalpy (H), is defined as U plus the product of pressure and volume. The change in enthalpy is equal to the heat absorbed at constant pressure, and because enthalpy is also a state function, its change is independent of the process path, a principle fundamental to Hess’s law of constant heat summation. The chapter defines heat capacity (C) as the ratio of thermal energy change to temperature change, noting that it must be specified at either constant volume (Cv) or constant pressure (Cp). For an ideal gas, both internal energy and enthalpy are solely functions of temperature, and the difference between the molar heat capacities at constant pressure and constant volume is equal to the gas constant R. In a reversible isothermal process for an ideal gas, the change in U is zero, meaning work performed equals heat absorbed (w equals q). Conversely, a reversible adiabatic process is defined by zero heat transfer (q equals 0), and the path of the state change is described by the relationship that pressure times volume raised to the power gamma (the ratio of Cp to Cv) equals a constant. The work term is generalized beyond simple pressure-volume work to include forms such as magnetic work on paramagnetic materials, electrical work on dielectric materials, and surface work required to create new surface area. The sign convention used throughout assigns a positive value to work done by the system and a positive value to heat absorbed by the system.