Thermodynamics

Heat and work are directional quantities, and thus the complete descriptionof a heat or work interaction requires the specification of both the magnitudeand direction. One way of doing that is to adopt a sign convention.The generally accepted formal sign convention for heat and work interactionsis as follows: heat transfer to a system and work done by a system arepositive; heat transfer from a system and work done on a system are negative.Another way is to use the subscripts in and out to indicate direction(Fig. 2–18). For example, a work input of 5 kJ can be expressed as W in 5kJ, while a heat loss of 3 kJ can be expressed as Q out 3 kJ. When thedirection of a heat or work interaction is not known, we can simply assumea direction for the interaction (using the subscript in or out) and solve for it.A positive result indicates the assumed direction is right. A negative result,on the other hand, indicates that the direction of the interaction is theopposite of the assumed direction. This is just like assuming a direction foran unknown force when solving a statics problem, and reversing thedirection when a negative result is obtained for the force. We will use thisintuitive approach in this book as it eliminates the need to adopt a formalsign convention and the need to carefully assign negative values to someinteractions.Note that a quantity that is transferred to or from a system during aninteraction is not a property since the amount of such a quantity depends onmore than just the state of the system. Heat and work are energy transfermechanisms between a system and its surroundings, and there are manysimilarities between them:1. Both are recognized at the boundaries of a system as they cross theboundaries. That is, both heat and work are boundary phenomena.2. Systems possess energy, but not heat or work.3. Both are associated with a process, not a state. Unlike properties, heator work has no meaning at a state.4. Both are path functions (i.e., their magnitudes depend on the path followedduring a process as well as the end states).Path functions have inexact differentials designated by the symbol d.Therefore, a differential amount of heat or work is represented by dQ ordW, respectively, instead of dQ or dW. Properties, however, are point functions(i.e., they depend on the state only, and not on how a system reachesthat state), and they have exact differentials designated by the symbol d. Asmall change in volume, for example, is represented by dV, and the totalvolume change during a process between states 1 and 2 is 2dV V 2 V 1 ¢V1That is, the volume change during process 1–2 is always the volume at state2 minus the volume at state 1, regardless of the path followed (Fig. 2–19).The total work done during process 1–2, however, is 2dW W 12 1not ¢W21SystemChapter 2 | 63SurroundingsQ inQ outW inW outFIGURE 2–18Specifying the directions of heat andwork.P12 m 3∆V A = 3 m 3 ; W A = 8 kJ∆V B = 3 m 3 ; W B = 12 kJProcess AProcess B25 m 3FIGURE 2–19Properties are point functions; but heatand work are path functions (theirmagnitudes depend on the pathfollowed).V