11.2.1 First Law of Thermodynamics

We begin with the application of the first law of thermodynamics, first to a closed system and then to an open system. A system is any bounded portion of the universe, moving or stationary, which is chosen for the application of the various thermodynamic equations. For a closed system, in which no mass crosses the system boundaries, the change in total energy of the system, , is equal to the heat flow to the system, δQ, minus the work done by the system on the surroundings, δW. For a closed system, the energy balance is

11-1

The δ’s signify that δQ and δW are not exact differentials of a state function.

The continuous-flow reactors we have been discussing are open systems in that mass crosses the system boundary. We shall carry out an energy balance on the open system shown in Figure 11-1. For an open system in which some of the energy exchange is brought about by the flow of mass across the system boundaries, the energy balance for the case of only one species entering and leaving becomes

11-2

Figure 11-1. Energy balance on a well-mixed open system: schematic.

Typical units for each term in Equation (11-2) are (Joule/s).

We will assume that the contents of the system volume are well mixed, an assumption that we could relax but that would require a couple of pages of text to develop, and the end result would be the same! The unsteady-state energy balance for an open well-mixed system that has n species, each entering and leaving the system at its respective molar flow rate F_i (moles of i per time) and with its respective energy E_i (joules per mole of i), is

11-3

We will now discuss each of the terms in Equation (11-3).