Thermodynamics

178 | ThermodynamicsVacuumP = 0W = 0(c) Under stated assumptions and observations, the energy balance on thesystem can be expressed asE in E out ¢E systemH2 OHeatFIGURE 4–16Expansion against a vacuum involvesno work and thus no energy transfer.1 kgIRON20 30°C4.5 kJ←1 kgWATER20 30°C41.8 kJFIGURE 4–17It takes different amounts of energy toraise the temperature of differentsubstances by the same amount.←Net energy transferby heat, work, and massChange in internal, kinetic,potential, etc., energiesNotice that even though the water is expanding during this process, the systemchosen involves fixed boundaries only (the dashed lines) and thereforethe moving boundary work is zero (Fig. 4–16). Then W 0 since the systemdoes not involve any other forms of work. (Can you reach the same conclusionby choosing the water as our system?) Initially,The quality at the final state is determined from the specific volumeinformation:ThenSubstituting yieldsx 2 v 2 v f 0.002 0.001 2.3 105v fg 43.34 0.001u 2 u f x 2 u fgu 1 u f @ 25°C 104.83 kJ>kg 104.83 kJ>kg 12.3 10 5 212304.3 kJ>kg2 104.88 kJ>kg⎫ ⎪⎬⎪⎭⎫⎪⎬⎪⎭Q in ¢U m 1u 2 u 1 2Q in 15 kg231104.88 104.832 kJkg4 0.25 kJDiscussion The positive sign indicates that the assumed direction is correct,and heat is transferred to the water.m = 1 kg∆T = 1°CSpecific heat = 5 kJ/kg ·°C5 kJFIGURE 4–18Specific heat is the energy required toraise the temperature of a unit mass ofa substance by one degree in aspecified way.INTERACTIVETUTORIALSEE TUTORIAL CH. 4, SEC. 3 ON THE DVD.4–3 SPECIFIC HEATSWe know from experience that it takes different amounts of energy to raisethe temperature of identical masses of different substances by one degree.For example, we need about 4.5 kJ of energy to raise the temperature of 1 kgof iron from 20 to 30°C, whereas it takes about 9 times this energy (41.8 kJto be exact) to raise the temperature of 1 kg of liquid water by the sameamount (Fig. 4–17). Therefore, it is desirable to have a property that willenable us to compare the energy storage capabilities of various substances.This property is the specific heat.The specific heat is defined as the energy required to raise the temperatureof a unit mass of a substance by one degree (Fig. 4–18). In general, thisenergy depends on how the process is executed. In thermodynamics, we areinterested in two kinds of specific heats: specific heat at constant volume c vand specific heat at constant pressure c p .Physically, the specific heat at constant volume c v can be viewed as theenergy required to raise the temperature of the unit mass of a substanceby one degree as the volume is maintained constant. The energy required to