Thermodynamics

Chapter 8 | 447Analysis We consider a general closed system (a fixed mass) that is free toexchange heat and work with its surroundings (Fig. 8–35). The system undergoesa process from state 1 to state 2. Taking the positive direction of heattransfer to be to the system and the positive direction of work transfer to befrom the system, the energy and entropy balances for this closed system canbe expressed asEnergy balance:E in E out ¢E system S Q W E 2 E 1WClosedsystemT bEntropybalance:2S in S out S gen ¢S system S a dQ T b S gen S 2 S 1boundary1QMultiplying the second relation by T 0 and subtracting it from the first one givesQ T 0 2a dQ T b W T 0 S gen E 2 E 1 T 0 1S 2 S 1 2boundary2However, the heat transfer for the process 1-2 can be expressed as Q dQand the right side of the above equation is, from Eq. 8–17, (X 2 X 1 ) P 0 (V 2 V 1 ). Thus, 2dQ T 0 2a dQ T b W T 0 S gen X 2 X 1 P 0 1V 2 V 1 211boundaryLetting T b denote the boundary temperature and rearranging give 211a 1 T 0T bb dQ 3W P 0 1V 2 V 1 24 T 0 S gen X 2 X 1(8–43)which is equivalent to Eq. 8–41 for the exergy balance except that the integrationis replaced by summation in that equation for convenience. Thiscompletes the proof.Discussion Note that the exergy balance relation above is obtained byadding the energy and entropy balance relations, and thus it is not an independentequation. However, it can be used in place of the entropy balancerelation as an alternative second law expression in exergy analysis.1FIGURE 8–35A general closed system considered inExample 8–9.EXAMPLE 8–10Exergy Destruction during Heat ConductionConsider steady heat transfer through a 5-m 6-m brick wall of a house ofthickness 30 cm. On a day when the temperature of the outdoors is 0°C, thehouse is maintained at 27°C. The temperatures of the inner and outer surfacesof the brick wall are measured to be 20°C and 5°C, respectively, andthe rate of heat transfer through the wall is 1035 W. Determine the rate ofexergy destruction in the wall, and the rate of total exergy destruction associatedwith this heat transfer process.Solution Steady heat transfer through a wall is considered. For specifiedheat transfer rate, wall surface temperatures, and environment conditions,the rate of exergy destruction within the wall and the rate of total exergydestruction are to be determined.Assumptions 1 The process is steady, and thus the rate of heat transferthrough the wall is constant. 2 The exergy change of the wall is zero during