南昌大学材料热力学答案(3)

brine , which is maintained at -20℃ by a refrigerator. The aluminum is being fed into the brine at a rate of one kilogram per minute. The refrigerator operates in an environment at 30℃; that is the refrigerator may reject heat at 30℃. what is them minus power rating in kilowatts, of motor required to operate the refrigerator? Data for aluminum heat capacity is 28J/mol K; Molecular weight 27g/mol Solution:PL?2728?(480??20)PW?TH?TLTLPL?30??20273?20PL?102474(W)?102.5(kW)1000

2.10 an electric power generating plant has a rated output of 100MW. The boiler of the plant operates at 300℃. The condenser operates at 40℃

(a) at what rate (joules per hour) must heat be supplied to the boiler?

(b) The condenser is cooled by water, which may under go a temperature rise of no more than 10℃. What

volume of cooling water in cubic meters per hour, is require to operate the plant?

(c) The boiler tempeture is to be raised to 540℃,but the condensed temperature and electric output will remain

the same. Will the cooling water requirement be increased, decreased, or remain the same? Data heat capacity 4.184, density 1g/cm3

(a)PH?THTH?TL8P?300?273300?40108(b)Solution:

?2.2?10(W)QH?PHt?7.9?10(J)11 QL?4.3?1011(J)V?10?10?4.184?QLV?1.03?10(m)436

(c)PH?THTH?TL8P?540?273540?40108?1.626?10(W)no

2.11 (a) Heat engines convert heat that is available at different temperature to work. They have been several proposals to generate electricity y using a heat engine that operate on the temperature differences available at different depths in the oceans. Assume that surface water is at 20℃, that water at a great depth is at 4℃, and that both may be considered to be infinite in extent. How many joules of electrical energy may be generated for each joule of energy absorbed from surface water? (b) the hydroelectric generation of electricity use the drop height of water as the energy source. in a particular region the level of river drops from 100m above sea level to 70m above the sea level . what fraction of the potential energy change between those two levels may be converted into electrical energy? how much electrical energy ,in kilowatt-hours, may be generated per cubic meter of water that undergoes such a drop? Solution:

(a)W?(b)P?TH?TLTHmg?h1000QH?20?420?2731?0.055(J)6

?3600?1.06?10(kW/h)2.12 a sports facility has both an ice rink and a swimming pool. to keep the ice frozen during the summer requires the removal form the rink of 105 KJ of thermal energy per hour. It has been suggested that this task be performed by a thermodynamic machine, which would be use the swimming pool as the high temperature reservoir. The ice in the rink is to be maintain at a temperature of –15℃, and the swimming pool operates at 20℃, (a) what is the theoretical minimum power, in kilowatts, required to run the machine? (b) how much heat , in joule per hour , would be supplied t the pool by this machine?

Solution:

(a)P?TH?TLTLPL?20?15273?15510/3600?3.77(kW)55

(b)QH?273?20273?1510?1.14?10(kJ)2.13

(a)2Al?N2?2AlNsolution:

(b)?H?152940(cal/mol)(c)?S?4.82?2?6.77?2?45.77??49.67(cal/molK)(d)?H?152940(cal/mol)?S?4.82?2?6.77?2?45.77?8.314ln10??68.81(cal/molK)

2.14

?S?m(?0CP,ICET?336273?10dT??HmTm40??0CP,WATERTdT)solution:

?(2.1ln273263?4.184ln273?40273

)12000?22574(J/K)2.15

W?TH?TLTLQL?300?77771000?2896(J)

W2?70428(J)2.16

W?W?TH?TLTLTH?TLTHQL?QH?300?4.24.2300?4.230083.3?5866.7(J)(83.3?1.5?8.314(300?4.2))?3719.4(J)

2.17

(a)?T?0?U?OQ??W?n??pdV?1?8.314?298ln10?5704(J)(b)?S?nRln(c)Q?0(d)yesP0P?1?8.314?ln10?19.1(J/K)

2.18

500?60?TH?TLTL335m?20?0273335m

m?1222(g)Property Relations

1. At -5?C, the vapor pressure of ice is 3.012mmHg and that of supercooled liquid water is 3.163mmHg. The latent heat of fusion of ice is 5.85kJ/mol at -5?C. Calculate ?G and ?S per mole for the transition of from water to ice at -5?C. (3.2, 94)

?G?RTlnPH2O,icePH2O,water3.0123.163Solution:

?8.314?(273?5)ln

?8.314?268?ln0.9523??108.9J/mol3?H?5.85?10J/mol

???G??H?T?S?S??H??GT?5850?(?108.9)268?22.23J/(mol?K)

2. (1) A container of liquid lead is to be used as a calorimeter to determine the heat of mixing of two metals, A and B. It has been determined by experiment that the “heat capacity” of the bath is 100cal/?C at 300?C. With the bath originally at 300?C, the following experiments are performed;(2) A mechanical mixture of 1g of A and 1g of B is dropped into the calorimeter. A and B were originally at 25?C. When the two have dissolved, the temperature of the bath is found to have increased 0.20?C. 2. Two grams of a 50:50(wt.%) A-B alloy at 25?C is dropped similarly into the calorimeter. The temperature decreases 0.40?C. (a) What is the heat of mixing of the 50?50 A-B alloy (per gram of alloy)? (b) To what temperature does it apply ? (3.5, 94) Solution: CP,bath?100cal/K?418J/mol (a) Q?CP,bath?T/2?100?0.2/2?10cal/g

This is the heat of mixing. (b) The heat capacity of CP, alloy : CP,alloy??CP,bath??T2?(300?0.4?25)100?0.42?274.6?0.072cal/(g?K)

Assuming that the calorimeter can be applied to the maximum of T?C, the for mixing to form 1 gram of alloy:

Q1?CP,bath(300?T')?10 , Q2?CP,alloy?(T?T'), Q1?Q2

CP,bath(300?T')?10?CP,alloy(T?T'

3. The equilibrium freezing point of water is 0?C. At that temperature the latent heat of fusion of ice (the heat required to melt the ice) is 6063J/mol. (a) What is the entropy of fusion of ice at 0?C ? (b) What is the change of Gibbs free energy for ice ?water at 0?C?(c) What is the heat of fusion of ice at -5?C ? CP(ice) = 0.5 cal/(g. ?C); CP(water) = 1.0 cal/(g. ?C). (d) Repeat parts a and b at -5?C. (3.6, p94) Solution: (a) At 0?C, ?G =0, ? Tm?S = ?H ?S??HTm?6030273?22.09J/(mol.K)

(b) At 0?C, ?G =0 ? CP,ice?0.5cal/(g.K)?0.5?4.18?18J/(mol.K)?37.62J/(mol.K) CP,water?1.0cal/(g.K)?1.0?4.18?18J/(mol.K)?75.24J/(mol.K) a reversible process can be designed as follows to do the calculation:

（1） （3） （2） Ice, 0?C water, 0?C ice, -5?C （4） water, -5?C ?Hfu??H??(1)??H(2)??H(3)268??273268273Cp,icedT??H??273Cp,waterdT268(Cp,ice?CP,water)dT??H

?(37.62?75.24)?5?6030?5841.9J/mol （d）

?S(4)??S(1)??S(2)??3(3)??Cp,iceTCp,waterT??273268273dT??S??268273dT(Cp,ice?CP,water)T

268dT??S?22.09?(37.62?75.24)?ln?21.39J/(mol.K)273268 ?G(4)??H(4)?T?S(4)?5841.9?268?21.39?109.38

4. (a) What is the specific volume of iron at 298K, in cubic peter per mole? (b) Derive an equation for the change of entropy with pressure at constant temperature for a solid, expressed in terms of physical quantities usually available, such as the ones listed as data; (c) The specific entropy of iron (entropy per mole )at 298K and a pressure of 100 atm is needed for a thermodynamic calculation. The tabulated “standard entropy”(at 298 K and a pressure of 1 atm) is

oS298?27.28J/K.mol. What percentage error would result if one assumed that the specific entropy at 298K and o100 atm were equal to the value of S298 given above ？

DATA：（for iron） Cp = 24 J K-1mol-1 Compressibility = 6 ? 10-7 atm –1

Linear coefficient of thermal expansion = 15 ? 10-6 ?C-1

Density = 7.87 g/cm3

Molecular weight = 55.85g/mol

Note: It may be possible to solve this problem with out using all the data given. (3.7, 95) Solution: (a)

Viron?molweightdensity?55.85g/mol7.87g/cm3?7.10cm3/mol?7.10?10?63m/mol

(b) ????S???V?

??????P?T??T?P??P?T?S? ???????V?V??3V?l

for iron:

??S??????3V??P?Tiron?l,iron?63

??3?7.10?10??3.2?10?10?15?10?6

(m/(mol.K))?Siron??3.2?10( c )

?10?P

?Siron??3.2?10??3.2?10?10?10(100?1)?1.013?10?99?1.013?10?5?5?5

??320.9?10??3.21?10?3(J/mol.K)error%??Siron?So298?100%??1.12?10?2

Equilibrium

1. At 400?C, liquid zinc has a vapor pressure of 10-4 atm. Estimate the boiling temperature zinc, knowing that

its heat of evaporation is approximately 28 kcal/mol. (4.2, P116) Solution: (a) VVice?18g/mol0.92g/cm?33?19.57cm/mol?19.57?103?63?63m/mol

18g/mol1g/cmwater?18cm/mol?18?10?63m/mol

3m/mol

?Vfus??1.57?10According to the Clapeyron equation:

dPdT???1?Vfus??HT?fus

fus??dP??1?Vfus??HTdTtake definite integration of the above:

?50?1.013?10551.013?10dP???H?Vfusfus?5T1T?273?dT

lnT273??V?Hfusfus?49?1.013?10?6??1.57?10?49?1.013?1060095

??0.013T?272.8K

(b)

P?1500.01?3?50?10lb/in.?50?10?6897Pa?345?10Pa3236

(c )

?P?345?106

lnT273??V?Hfusfus?345?10?66??1.57?10?345?106T?249.46K6009??0.09

1. At 400?C, liquid zinc has a vapor pressure of 10-4 atm. Estimate the boiling temperature of zinc, knowing that

its heat of vaporation is approximately 28kcal/mol. (4.3,117)

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