Thermodynamics

Chapter 6 | 293High-temperature reservoirat T HHigh-temperature reservoirat T HQ HHEATENGINEη th = 100%Q H + Q L= Q HQ L ERATORERATORQ LW netREFRIG-REFRIG-Q LLow-temperature reservoirat T L(a) A refrigerator that is powered bya 100 percent efficient heat engineLow-temperature reservoirat T L(b) The equivalent refrigeratorFIGURE 6–27Proof that the violation of theKelvin–Planck statement leads to theviolation of the Clausius statement.Consider the heat-engine-refrigerator combination shown in Fig. 6–27a,operating between the same two reservoirs. The heat engine is assumed tohave, in violation of the Kelvin–Planck statement, a thermal efficiency of100 percent, and therefore it converts all the heat Q H it receives to work W.This work is now supplied to a refrigerator that removes heat in the amountof Q L from the low-temperature reservoir and rejects heat in the amount ofQ L Q H to the high-temperature reservoir. During this process, the hightemperaturereservoir receives a net amount of heat Q L (the differencebetween Q L Q H and Q H ). Thus, the combination of these two devices canbe viewed as a refrigerator, as shown in Fig. 6–27b, that transfers heat in anamount of Q L from a cooler body to a warmer one without requiring anyinput from outside. This is clearly a violation of the Clausius statement.Therefore, a violation of the Kelvin–Planck statement results in the violationof the Clausius statement.It can also be shown in a similar manner that a violation of the Clausiusstatement leads to the violation of the Kelvin–Planck statement. Therefore,the Clausius and the Kelvin–Planck statements are two equivalent expressionsof the second law of thermodynamics.6–5 ■ PERPETUAL-MOTION MACHINESWe have repeatedly stated that a process cannot take place unless it satisfiesboth the first and second laws of thermodynamics. Any device that violateseither law is called a perpetual-motion machine, and despite numerousattempts, no perpetual-motion machine is known to have worked. But thishas not stopped inventors from trying to create new ones.A device that violates the first law of thermodynamics (by creatingenergy) is called a perpetual-motion machine of the first kind (PMM1),and a device that violates the second law of thermodynamics is called aperpetual-motion machine of the second kind (PMM2).INTERACTIVETUTORIALSEE TUTORIAL CH. 6, SEC. 5 ON THE DVD.