Thermodynamics

Weights and Measures held in 1954, the triple point of water (the state atwhich all three phases of water exist in equilibrium) was assigned the value273.16 K (Fig. 6–45). The magnitude of a kelvin is defined as 1/273.16 ofthe temperature interval between absolute zero and the triple-point temperatureof water. The magnitudes of temperature units on the Kelvin andCelsius scales are identical (1 K 1°C). The temperatures on these twoscales differ by a constant 273.15:(6–17)Even though the thermodynamic temperature scale is defined with the helpof the reversible heat engines, it is not possible, nor is it practical, to actuallyoperate such an engine to determine numerical values on the absolute temperaturescale. Absolute temperatures can be measured accurately by other means,such as the constant-volume ideal-gas thermometer together with extrapolationtechniques as discussed in Chap. 1. The validity of Eq. 6–16 can bedemonstrated from physical considerations for a reversible cycle using anideal gas as the working fluid.6–10 ■ THE CARNOT HEAT ENGINEThe hypothetical heat engine that operates on the reversible Carnot cycle iscalled the Carnot heat engine. The thermal efficiency of any heat engine,reversible or irreversible, is given by Eq. 6–6 aswhere Q H is heat transferred to the heat engine from a high-temperaturereservoir at T H , and Q L is heat rejected to a low-temperature reservoir at T L .For reversible heat engines, the heat transfer ratio in the above relation canbe replaced by the ratio of the absolute temperatures of the two reservoirs,as given by Eq. 6–16. Then the efficiency of a Carnot engine, or anyreversible heat engine, becomes(6–18)This relation is often referred to as the Carnot efficiency, since theCarnot heat engine is the best known reversible engine. This is the highestefficiency a heat engine operating between the two thermal energy reservoirsat temperatures T L and T H can have (Fig. 6–46). All irreversible (i.e.,actual) heat engines operating between these temperature limits (T L and T H )have lower efficiencies. An actual heat engine cannot reach this maximumtheoretical efficiency value because it is impossible to completely eliminateall the irreversibilities associated with the actual cycle.Note that T L and T H in Eq. 6–18 are absolute temperatures. Using °C or°F for temperatures in this relation gives results grossly in error.The thermal efficiencies of actual and reversible heat engines operatingbetween the same temperature limits compare as follows (Fig. 6–47):h th •T 1°C2 T 1K2 273.15h th 1 Q LQ Hh th,rev 1 T LT H6 h th,rev irreversible heat engine h th,rev reversible heat engine7 h th,rev impossible heat engine(6–19)Chapter 6 | 305Heat reservoirTCarnotHEQ HQ L273.16 K (assigned)Water at triple pointT = 273.16 –––Q HQ LFIGURE 6–45A conceptual experimental setup todetermine thermodynamictemperatures on the Kelvin scale bymeasuring heat transfers Q H and Q L .INTERACTIVETUTORIALSEE TUTORIAL CH. 6, SEC. 10 ON THE DVD.High-temperature reservoirat T H = 1000 KQ HCarnotHEη th = 70%Q LLow-temperature reservoirat T L = 300 KWW net,outFIGURE 6–46The Carnot heat engine is the mostefficient of all heat engines operatingbetween the same high- and lowtemperaturereservoirs.