Principles of naval engineering - Historic Naval Ships Association

VChapter 8-INTRODUCTION TO THERMODYNAMICSOne is the general conduction equationQ = kTA 4-^2where, as we have seen, Q may be expressedin calories or in Btu. In this example, we areusing the metric CGS system and must thereforeexpress ^in calories. The second equation wewill use gives us a second way of calculatingQ— that is, by determining the amount of heatabsorbed by the circulating water. Thus,Q =mass of water x temperature changeof water x specific heat of waterSubstituting some of our known values inthis second equation, we find thatQ = (1300) (10) (1) = 13,000 caloriesUsing this value of Q and substituting otherknown values in the general conduction equation,we find that13,000 = k (360) (20) (80 - 60 )100.9 = k= k (360) (20) (2)= 14,400 kIt should be noted that the general conductionequation applies only when there is a steadystatethermal gradient— that is, after a uniformflow of heat has been established. It should benoted also that k_ varies slightly as a function oftemperature, although for many purposes therise in }^that goes with a rise in temperatureis so slight that it can safely be disregarded.In considering the experimental determinationof thermal conductivity, why do we include"specific heat of water = 1.00" as one of theknown data? What is specific heat, and what isits utility? Specific heat (also called heat capacityor specific heat capacity) is, like thermalconductivity, a thermal property of matter thatmust be determined experimentally for eachsubstance. In general, we may say that specificheat is the property of matter that explains whythe addition of equal quantities of heat to twodifferent substances will not necessarily producethe same temperature rise in the two substances.We may define the specific heatof any substanceas the quantity of heat required to raise thetemperature of unit mass of that substance 1degree. ^ In the metric CGS system, specificheat is expressed in calories per gram perdegree Celsius; in the metric MKS system, itis expressed in kilocalories per kilogram perdegree Celsius; and in British systems, it isexpressed in Btu per pound per degree Fahrenheit.The specific heat of water is 1.00 in anysystem, and the numerical value of specificheat for any given substance is the same in allsystems (although the units are, of course, different).Specific heat is determined experimentallyby laboratory procedures which are extremelycomplex and difficult in practice, althoughbasically simple in theory. One of the commonestmethods of determining specific heat isknown as the method of mixtures. In this procedure,a known mass of finely divided metal isheated and then mixed with a known mass ofwater. The temperatures of the metal beforemixing, of the water before mixing, and of themixture just as it reaches thermal equilibriumare measured. Then, on the simple premise thatthe heat lost by one substance must be gainedby the other substance, the specific heat of themetal can be found by using the equationm^c^ (tl -*3^ ='"2^2^*3-wherem- = mass of metalm„ = mass of waterc^- specific heat of metalc„ = specific heat of water (known to be 1.00)t- . temperature of metal before mixingt„ = temperature of water before mixingt„ = temperature at which water and metalreach thermal equilibriumSpecific heat as defined here should not be confusedwith the relatively useless concept of specific heatratio , by which the heat capacity of each substance iscompared to the heat capacity of water (taken as 1.00).The specific heat ratio is, obviously, a pure numberwithout units.165