Thermodynamics

400 | Thermodynamicsambient in a liquid-to-air heat exchanger. This heat rejected usually amountsto 60 to 90 percent of the power input, and thus it represents a huge amountof energy that can be used for a useful purpose such as space heating in winter,preheating the air or water in a furnace, or other process-related purposes(Fig. 7–80). For example, assuming 80 percent of the power input is convertedto heat, a 150-hp compressor can reject as much heat as a 90-kWelectric resistance heater or a 400,000-Btu/h natural gas heater when operatingat full load. Thus, the proper utilization of the waste heat from a compressorcan result in significant energy and cost savings.SUMMARYThe second law of thermodynamics leads to the definition ofa new property called entropy, which is a quantitative measureof microscopic disorder for a system. Any quantitywhose cyclic integral is zero is a property, and entropy isdefined asdS a dQ T b int revFor the special case of an internally reversible, isothermalprocess, it gives¢S Q T 0The inequality part of the Clausius inequality combined withthe definition of entropy yields an inequality known as theincrease of entropy principle, expressed asS gen 0where S gen is the entropy generated during the process.Entropy change is caused by heat transfer, mass flow, andirreversibilities. Heat transfer to a system increases theentropy, and heat transfer from a system decreases it. Theeffect of irreversibilities is always to increase the entropy.The entropy-change and isentropic relations for a processcan be summarized as follows:1. Pure substances:Any process:¢s s 2 s 1Isentropic process: s 2 s 12. Incompressible substances:T 2Any process:s 2 s 1 c avg ln T 1Isentropic process: T 2 T 13. Ideal gases:a. Constant specific heats (approximate treatment):Any process:Isentropic process:T 2s 2 s 1 c v,avg ln R ln T 1T 2s 2 s 1 c p,avg ln R lnT 1a T 2b a v k11bT 1 sconst. v 2a T 2b a P 1k12>k2bT 1 sconst. P 1a P 2b a v k1bP 1 sconst. v 2b. Variable specific heats (exact treatment):Any process:P 2P 1P 2s 2 s 1 s° 2 s° 1 R ln P 1v 2v 1