Thermodynamics

7–51E A 1.2-ft 3 well-insulated rigid can initially containsrefrigerant-134a at 140 psia and 70°F. Now a crack developsin the can, and the refrigerant starts to leak out slowly,Assuming the refrigerant remaining in the can has undergonea reversible, adiabatic process, determine the final mass inthe can when the pressure drops to 20 psia.R-134a140 psia70°FFIGURE P7–51EEntropy Change of Incompressible Substances7–52C Consider two solid blocks, one hot and the othercold, brought into contact in an adiabatic container. After awhile, thermal equilibrium is established in the container as aresult of heat transfer. The first law requires that the amountof energy lost by the hot solid be equal to the amount ofenergy gained by the cold one. Does the second law requirethat the decrease in entropy of the hot solid be equal to theincrease in entropy of the cold one?7–53 A 50-kg copper block initially at 80°C is dropped intoan insulated tank that contains 120 L of water at 25°C. Determinethe final equilibrium temperature and the total entropychange for this process.Chapter 7 | 405and the total entropy change for this process. Answers:168.4°C, 0.169 kJ/K7–56 Reconsider Prob. 7–55. Using EES (or other)software, study the effect of the mass of the ironblock on the final equilibrium temperature and the totalentropy change for the process. Let the mass of the iron varyfrom 1 to 10 kg. Plot the equilibrium temperature and thetotal entropy change as a function of iron mass, and discussthe results.7–57 A 50-kg iron block and a 20-kg copper block, bothinitially at 80°C, are dropped into a large lake at 15°C. Thermalequilibrium is established after a while as a result of heattransfer between the blocks and the lake water. Determine thetotal entropy change for this process.IRON50 kgLAKE 15°CCOPPER20 kgFIGURE P7–577–58 An adiabatic pump is to be used to compress saturatedliquid water at 10 kPa to a pressure to 15 MPa in a reversiblemanner. Determine the work input using (a) entropy data fromthe compressed liquid table, (b) inlet specific volume andpressure values, (c) average specific volume and pressure values.Also, determine the errors involved in parts (b) and (c).Water15 MPaCopper50 kg10 kPaPump120 LFIGURE P7–537–54 A 25-kg iron block initially at 350°C is quenched inan insulated tank that contains 100 kg of water at 18°C.Assuming the water that vaporizes during the process condensesback in the tank, determine the total entropy changeduring this process.7–55 A 20-kg aluminum block initially at 200°C is broughtinto contact with a 20-kg block of iron at 100°C in an insulatedenclosure. Determine the final equilibrium temperatureFIGURE P7–58Entropy Change of Ideal Gases7–59C Prove that the two relations for entropy change ofideal gases under the constant-specific-heat assumption (Eqs.7–33 and 7–34) are equivalent.7–60C Starting with the second T ds relation (Eq. 7–26),obtain Eq. 7–34 for the entropy change of ideal gases underthe constant-specific-heat assumption.7–61C Some properties of ideal gases such as internalenergy and enthalpy vary with temperature only [that is, u u(T) and h h(T)]. Is this also the case for entropy?