材料热力学习题答案1

(3)?H?0.086[393513?110523?(57?34?0.5?33)?T]?0.029[241604?(50?34?0.5?29)?T]?0.714?39.2(?T?402)?0.286?34?T?0?T?42594?1121(K),T?1419(K)38

12．A bath of molten copper is super cooled to 5℃ below its true melting point. Nucleation of solid copper then takes place, and the solidification proceeds under adiabatic conditions. What percentage of the bath solidifies?

DATA: Heat of fusion for copper is 3100 cal/mol at 1803℃(the melting point of copper) CP,L=7.5(cal/mol℃), CP,S=5.41+(1.5*10-3T )(cal/mol℃) （1.12） Solution

HLS,1803??18031798CP,SdT??17981803SCP,LdT?HL,1798?0

L?322HS(cal/mol),1798?3100?5.41?5?1.5?10(1803?1798)?0.5?7.5?5?3103

13．Cuprous oxide (Cu2O) is being reduced by hydrogen in a furnace at 1000K, (a)write the chemical reaction for the reduced one mole of Cu2O

(b)how much heat is release or absorbed per mole reacted? Given the quantity of heat and state whether heat is evolved (exothermic reaction) or absorbed (endothermic reaction)

DATA: heat of formation of 1000K in cal/mol Cu2O=-41900 H2O=-59210 （1.13） solution

Cu2O?H2?Cu?H2O?H?59210?41900?17310(cal/mol),exothermic reaction

14. (a) what is the enthalpy of pure, liquid aluminum at 1000K?

(b) an electric resistance furnace is used to melt pure aluminum at the rate of 100kg/h. the furnace is fed with solid aluminum at 298K. The liquid aluminum leaves the furnace at 1000K. what is the minimum electric powder rating (kW) of furnace.

DATA : For aluminum : atomic weight=27g/mol, Cp,s=26(J/molK), Cp,L=29(J/molK), Melting point=932K, Heat of fusion=10700J/mol (1.14)

Hl,1000??CP,SdT??2989321000932SCP,LdT?HL(J/mol) Solution?26?(932?298)?29?(1000?932)?10700?27184P?271841?1000??279.7(W)?0.28(kW)273600

15 A waste material (dross from the melting of aluminum) is found to contain 1 wt% metallic aluminum. The rest may be assumed to aluminum oxide. The aluminum is finely divided and dispersed in the aluminum oxide; that is the two material are thermally connected.

If the waster material is stored at 298K. what is the maximum temperature to which it may rise if all the metallic aluminum is oxidized by air/ the entire mass may be assumed to rise to the same temperature. Data : atomic weight Al=27g/mol, O=16g/mol, Cp,s,Al=26(J/molK), Cp,s,

Al2O3=104J/mol, heat formation of Al2O3=-1676000J/mol (1.15)

1?27?2Solution;?T?302(K)T?600(K)1676000?1?16?1.5?27?9927?104??T102

16 Metals exhibit some interesting properties when they are rapidly solidified from the liquid state. An apparatus for the rapid solidification of copper is cooled by water. In the apparatus, liquid copper at its melting point (1356K) is sprayed on a cooling surface, where it solidified and cools to 400K. The copper is supplied to the apparatus at the rate of one kilogram per minute. Cooling water is available at 20℃, and is not allowed to raise above 80℃. What is the minimum flow rate of water in the apparatus, in cubic meters per minute?

DATA; for water: Cp=4.184J/g k, Density=1g/cm3; for copper: molecular weight=63.54g/mol Cp=7cal/mol k, heat of fusion=3120 cal/mol (1.16)

QCopper/min?[3120?7?(1356?400)]?Solution:QWater/min?1(80?20)V100063.54?min

V?2.573?10?3(m3/min)

17 water flowing through an insulated pipe at the rate of 5L/min is to be heated from 20℃ to 60℃ b an electrical resistance heater. Calculate the minimum power rating of the resistance heater in watts. Specify the system and basis for you calculation. DATA; For water Cp=4.184J/g k, Density=1g/cm3 (1.17)

Solution: W?4.184?(60?20)?5?1000?13947(W) 60

18 The heat of evaporation of water at 100℃ and 1 atm is 2261J/mol (a) what percentage of that energy is used as work done by the vapor?

(b)if the density of water vapor at 100℃ and 1 atm is 0.597kg/m3 what is the internal energy change for the evaporation of water? (1.18)

P?V?101325?Solution: %?373?0.0224?3101(J/mol)2733101?7.6%

2261?18?U?W?Q??3101?2261?18?37597(J/mol)

19 water is the minimum amount of steam (at 100℃ and 1 atm pressure) required to melt a kilogram of ice (at 0℃)? Use data for problem 1.20 (1.19) Solution m(2261?4.18?100)?1000?334,m?125(g)

20 in certain parts of the world pressurized water from beneath the surface of the earth is available as a source of thermal energy. To make steam, the geothermal water at 180℃ is passed through a flash evaporator that operates at 1atm pressure. Two streams come out of the evaporator, liquid water and water vapor. How much water vapor is formed per kilogram of geothermal water? Is the process reversible? Assume that water is incompressible. The vapor pressure of water at 180℃ is 1.0021 Mpa( about 10 atm) Data: CP,L=4.18J/(g k), CP,v=2.00J/(g k), △HV=2261J/g, △Hm=334 J/g (1.20) Solution:

(2261?2?80?4.18?80)x?4.18?80?(1000?x),x?138(g)irreversible