Law First Introduction to Terms: The First Law of thermodynamics can be expressed in either of two equivalent forms, both of which convey the essential nature of the law, to wit: conservation of energy in an isolated system (aka universe).
Euniv
Esys
Esurr
q w 0
The subscripts refer to "universe", "system", and "surroundings" respectively. Let us examine each term. Delta E ( E): Denotes the change in internal energy during a chemical/physical process. Units of Joules (J). The capital letter denotes that the internal energy is a "state function". This means that the change in internal energy (like potential energy) depends only on the initial and final states of the process (e.g. reactants and products). That is, E E f Ei . In other words, one simply subtracts the internal energy of the initial state from that of the final state to obtain the change. For those with interest in mathematics, this is related to exact differentials:
x2
dxf ( x)
x1
F ( x2 ) F ( x1 ) where F(x) is the anti-derivative of f(x). That is to say, the
integral is "replaced" by a function evaluation at the endpoints (the function being the anti-derivative of f(x). Note that if E is positive, Ef > Ei, and the energy of the system increases. Heat (q): Denotes the energy exchange between system and surroundings mediated by a difference in temperature; we call this energy exchange "heat". Note, this is part of the "gradual unfolding of a series of lies." Units of Joules (J). The use of the lower case letter denotes that "heat" is a "path function". This form of energy exchange will vary depending on the conditions and constraints taken in going from initial to final state (see text page 70 and file on this topic). For example, chemical processes taking place in a thermos allow no exchange of energy in the form of heat (q = 0 and we call such processes adiabatic). The sign convention is that q + denotes energy flow in the form of heat into the system; q denotes an energy flow out of the system. For the mathematically inclined, q is not an exact differential and its integral cannot be evaluated as above, but rather as a path integral q
dq .
path
What this means on a practical level is that an equilibrium system has no "heat" and we do not evaluate "changes heat". in "Heat" is only defined for a change in state. Thus, there is no "delta q" and we do not say that "the flask of solution has a heat ..."
Work (w): Denotes the energy exchange between system and surroundings mediated by an applied force; we call this energy exchange "work". This applied force can be mechanical; chemical; magnetic; electrical. In this class, work will be almost exclusively due to mechanical forces related to changes of volume against external pressures (see p. 72 of text) arising from net production or consumption of gases in chemical reactions. Units of Joules (J). The use of the lower case letter denotes that "work" is a "path function". This form of energy exchange will vary depending on the conditions and constraints taken in going from initial to final state (see text page 70 and file on this topic). For example, chemical processes taking place at constant volume (a rigid container) allow no exchange of energy in the form of work at least no mechanical work (w = 0 and we call such processes isochoric). The sign convention is that w + denotes energy flow in the form of work into the system; w denotes an energy flow out of the system. NOTA BENE: This sign convention is opposite that used in engineering. Quite reasonably, engineers are interested in extracting energy in the form of work from engines and hence have a sign convention denoting this energy extraction as positive. Don't shoot me, I'm just the messenger. For the mathematically inclined, w is not an exact differential and its integral cannot be evaluated as above, but rather as a path integral w
dw .
path
What this means on a practical level is that an equilibrium system has no "work" and we do not evaluate "changes in work". "Work" is only defined for a change in state. Thus, there is no "delta w" and we do not say that "the flask of solution has a work ..." The form of the first law, E = q + w, then, simply summarizes the two "forms" of energy exchange between the system and surroundings. Read: "the change in internal energy of a system (or surroundings or universe) equals the algebraic sum of the energy transfers to/from the system (surrounding or universe) in the forms of heat and work."