Thermodynamics

2dQS heat T Q ka T k(7–72)Chapter 7 | 379When the temperature T is not constant, the entropy transfer during aprocess 1-2 can be determined by integration (or by summation if appropriate)as1where Q k is the heat transfer through the boundary at temperature T k at locationk.When two systems are in contact, the entropy transfer from the warmersystem is equal to the entropy transfer into the cooler one at the point ofcontact. That is, no entropy can be created or destroyed at the boundarysince the boundary has no thickness and occupies no volume.Note that work is entropy-free, and no entropy is transferred by work.Energy is transferred by both heat and work, whereas entropy is transferredonly by heat. That is,Entropy transfer by work: S work 0(7–73)The first law of thermodynamics makes no distinction between heat transferand work; it considers them as equals. The distinction between heat transferand work is brought out by the second law: an energy interaction that isaccompanied by entropy transfer is heat transfer, and an energy interactionthat is not accompanied by entropy transfer is work. That is, no entropy isexchanged during a work interaction between a system and its surroundings.Thus, only energy is exchanged during work interaction whereas bothenergy and entropy are exchanged during heat transfer (Fig. 7–59).Entropygenerationvia frictionEntropy is nottransferredwith workFIGURE 7–59No entropy accompanies work as itcrosses the system boundary. Butentropy may be generated within thesystem as work is dissipated into a lessuseful form of energy.2 Mass FlowMass contains entropy as well as energy, and the entropy and energy contentsof a system are proportional to the mass. (When the mass of a systemis doubled, so are the entropy and energy contents of the system.) Bothentropy and energy are carried into or out of a system by streams of matter,and the rates of entropy and energy transport into or out of a system areproportional to the mass flow rate. Closed systems do not involve any massflow and thus any entropy transfer by mass. When a mass in the amount ofm enters or leaves a system, entropy in the amount of ms, where s is thespecific entropy (entropy per unit mass entering or leaving), accompanies it(Fig. 7–60). That is,Entropy transfer by mass flow: S mass ms(7–74)Therefore, the entropy of a system increases by ms when mass in theamount of m enters and decreases by the same amount when the sameamount of mass at the same state leaves the system. When the properties ofthe mass change during the process, the entropy transfer by mass flow canbe determined by integration fromhs mControl volumemhmsFIGURE 7–60Mass contains entropy as well asenergy, and thus mass flow into or outof system is always accompanied byenergy and entropy transfer.S # mass A csrV n dA c andS mass s dm ¢tS # mass dt(7–75)where A c is the cross-sectional area of the flow and V n is the local velocitynormal to dA c .