The problems of the first law
1.1 a lead bullet is fired at a frigid surface. At what speed must it travel to melt on impact, if its initial temperature is 25℃ and heating of the rigid surface of the rigid surface is neglected? The melting point of lead is 327℃. The molar heat of fusion of the lead is 4.8kJ/mol. The molar heat capacity CP of lead may be taken as 29.3J/(mol K)
Qabsorb?Qincrease?Qmelt?n(Cp?T??Hmelting)1212Solution:
W?mv2?nMv2
12Qabsorb?Wn[29.3?(327?25)?4.8?10]?V?363(m/s)3n207.2?10?3v21.2 what is the average power production in watts of a person who burns 2500 kcal of food in a day? Estimate the average additional powder production of 75Kg man who is climbing a mountain at the rate of 20 m/min
QBurning?2500?10?4.1868?10467000(J)SolutionP?W/t?QBurning/t?31046700024?60?602060?121(J/S)
Pincreasing?mg?ht?75?9.8??245(J/S) 1.3 One cubic decimeter (1 dm3) of water is broken into droplets having a diameter of one micrometer (1 um) at 20℃.
(a) what is the total area of the droplets?
(b) Calculate the minimum work required to produce the droplets. Assume that the droplets are rest (have zero
velocity)
Water have a surface tension of 72.75 dyn/cm at 20℃ (NOTES: the term surface energy (ene/cm2) is also used for surface tension dyn/cm)
Stotal?nSSingle?(1?1043?13)Solution
?4???(0.5?10?6?6)?6?10(m)232???(0.5?10?5?2)33
W???S?72.75?10?(3?10?6?10?2)?436.6(J)1.4 Gaseous helium is to be used to quench a hot piece of metal. The helium is in storage in an insulated tank with a volume of 50 L and a temperature of 25℃, the pressure is 10 atm. Assume that helium is an ideal gas.
(a) when the valve is opened and the gas escapes into the quench chamber (pressure=1 atm), what will be the
temperature of the first gas to hit the specimen?
(b) As the helium flows, the pressure in the tank drops. What will be the temperature of the helium entering the
quench chamber when the pressure in the tank has fallen to 1 atm?
(a)AdiabaticSolution: T?(P)R/CT0P0T?298?((b)?T?WnCpP
)0.4110?118(K)?1?(500?5)?101325?1010?50?101325?10R?298?3?3?118(K)?2.5RT?T0??T?298?118?180(K)1.5 An evacuated (P=0), insulted tank is surrounded by a very large volume (assume infinite volume) of an ideal gas at a temperature T0. The valve on the tank is oeened and the surrounding gas is allowed to flow suickly into t(e tank until the pressure insi`e the tank is equals the pressure outside. Assume that no heat flow takes place. What is the0final tempeture kf tèe gaS in the tank? The heat cap!city mf the gas, Cp and Cv each íay be(assumed to be c/nsuant over th? temperature rang!spanNed by the d?periment. You answer may be meft in terms of Cp and SvMhint: one way to approach the xroblem is to define the system as the gas ends up in the tank. hint: one way to approach the xroblem is to define the system as the gas ends up in the tank.
Adiabaticsolution TT0?(PP0)R/CP
T?T0(P0?0P0)R/CP?T01.6 Calculate the heat of reaction of methane with oxygen at 298K, assuming that the products of reaction are CO2 and CH4 (gas)[This heat of reaction is also called the low calorific power of methane] convert the answer into unites of Btu/1000 SCF of methane. SCF means standard cubic feet, taken at 298 and 1atm NOTE: this value is a good approximation for the low calorific powder of natural gas
FOR?H298[Kcal/g?mol]
0DATA: CH4(g) ?17.89CO2(g)?94.05H2O(g)?57.801.7
191.76?1010?33solution
CH4?2O2?CO2?2H2O?H298??(?HCO2?2?HH2O??HCH4)??(?94.05?2?57.80?17.89)?H298?191.76(Kcal/g?mol)??10.30483?10?252?1033?26.9(Btu/1000SCF)Methane is delivered at 298 K to a glass factory, which operates a melting furnace at 1600 K. The fuel is mixed with a quantity of air, also at 298 K, which is 10% in excess of the amount theoretically needed for complete combustion (air is approximately 21% O2 and 79% N2)
(a) Assuming complete combustion, what is the composition of the flue gas (the gas following combustion)? (b) What is the temperature of the gas, assuming no heat loss?
(c) The furnace processes 2000kg of glass hourly, and its heat losses to the surroundings average 400000 kJ/h.
calculate the fuel consumption at STP (in m3/h) assuming that for gas H1600-H298=1200KJ/KG
(d) A heat exchanger is installed to transfer some of the sensible heat of the flue gas to the combustion air.
Calculate the decrease in fuel consumption if the combustion air is heated to 800K DATA STP means T=298K, P=1atm
forCHCO42CP(cal/mol?C)?H2ON2O2
1613.711.98.28.2
(a)CH4?2O2?CO2?2H2O17921?8.71%?2?(1.1?1)CO2%?3?2?1.1?Solution
H2O%?2CO2%?17.43%N2%?72.12%O2%?0.87%(b)Cp,p?
?Cp,iXi?0.01[13.7?8.71?11.9?17.43?8.2?(72.12?0.87)]?9.25(cal/mol?C)191.76?10009.25?11.48?2104(K)?T?T0??T?298?(C)P?1200?2000?400000?2800000(KJ/h)VConsuming3?(2800000?1011.4810021p,r,i191.76?1000?9.25?11.48(1600?298)?4.1868?10.0224?3214(m/h))3(d)Cp,r?
?Cp,iXi?[16?8.2?2.2?]/11.48?8.87(cal/mol?C)ni)dT??H??H298??(?Cp,p,ini??C?191.76?1000?[(9.25?11.48)?8.87?11.48)](800?298)?189570(cal/g?mol)VConsuming?(2800000?1011.483189570?9.25?11.48(1600?800)?4.1868?10.0224?1644(m/h))31.8 In an investigation of the thermodynamic properties of a-manganese, the following heat contents were determined:
H700-H298=12113 J/(g atom) H1000-H298=22803 J/(g atom)
Find a suitable equation for HT-H298 and also for CP as a function of temperature in the form (a+bT) Assume that no structure transformation takes place in the given tempeture rang.
?H?b2?CPdT?b2?a?bTdT?[aT?22T]2982Ta(700?298)?(700?298)?121132Solution
a(1000?298)?a?35.62b??0.011b2(1000?298)?228032
CP?35.62?0.011T?H298?35.62(T?298)?0.0055(TT2?298)21.9 A fuel gas containing 40% CO, 10% CO2, and the rest N2 (by volume) is burnt completely with air in a furnace. The incoming and ongoing temperatures of the gases in the furnace are 773K and 1250K,respectively. Calculate (a) the maximum flame temperature and (b) heat supplied to the furnace per cu. ft of exhaust gas ?H?H0f,298,CO0f,298,CO2??110458J/mol??393296J/mol?3
CP,CO?28.45?3.97?10T?0.42?10TT?8.37?10T555?2(J/molK)(J/molK)
CP,CO2?44.35?9.20?10CP,O2?19.92?4.10?10?3?2?3T?1.67?10T?3?2(J/molK)CP,N2?29.03?4.184?10T(J/molK)2CO?O2?2COwhenthenreationCO?20%CO221molefuelneed1moleair(N2/O2?4)?5%N2?65%O2?10%productionCO2?27.8%N2?72.2%?H(a)Cp,r?i,298???Hp,p,i0f,298,rni???H0f,298,pni?393296?110458?282838(J/mol)?C?C?ni?0.2CP,CO?0.05CP,CO2?0.65CP,N2?0.1CP,O2?3?28.77?4.38?10Cp,r?p,p,iT?0.67?10T5?2(J/molK)ni?0.278CP,CO2?0.722CP,N2?3?33.28?5.58?10?H??Hi,298T?0.19?10T5?2(J/molK)p,r,ini??(?Cp,p,ini??Cni)dT5?2?282838?0.2?T?T298(33.28?5.58?10?3?3T?0.19?10T)?0.9dT??28.77733?4.38?10T?0.67?10T?35?2dT?0.67?10T5?1?28283.8?2?(28.77T?2.19?10T2)733298Solution
?(1.18T?0.321TT??2?0.499T?1)T298?0
?H???Hi,298ni??(?Cp,p,ini??Cp,r,ini)dT5?2?282838?0.2?T?T298(33.28?5.58?10?3?3T?0.19?10T)?0.9dT??28.77?4.38?1012502T?0.67?10T?35?2dT5?1?28283.8?2?(28.77T?2.19?10?(1.18T?0.321T?0.499TT?(b)Q298??282838?0.2?Q298??282838?0.2?125012501250?1T?0.67?10T2)1250298
)T298?0??2981250(33.28?5.58?10(33.28?5.58?10?3T?0.19?10TT?0.19?10T55?2)?0.9dT)?0.9dT?3?22981.10 (a) for the reaction CO?12O2?CO2,what is the enthalpy of reaction (?H0) at 298 K ?
(b) a fuel gas, with composition 50% CO, 50% N2 is burned using the stoichiometric amount of air. What is the composition of the flue gas?
(c) If the fuel gas and the air enter there burner at 298 K, what is the highest temperature the flame may attain
(adiabatic flame temperature)? DATA :standard heats of formation ?Hf at 298 K
CO??110000(J/mol)CO2??393000(J/mol)
Heat capacities [J/(mol K)] to be used for this problem N2=33, O2=33, CO=34, CO2=57
(a)?H0???H0f,298,rni???H0f,298,Pni??110000?393000?283000(J/mol)(b)fuelCO%?0.51?0.25/0.222.2100?11.1?22.2%,N2%?66.6%,O2%?11.1%?25%,N2%?75%,Solution productCO2%?
(C)Cp,P?Cr,P??Ci,r,P0i,p,PXi?33?0.666?33?0.222?34?0.111?33(J/mol?K)?CXi?57?0.25?33?0.75?39(J/mol?K)npCp,PdT?0?H??H??283000?0.222?(0.889?39)(T?298)?0T?2110(K)1.11 a particular blast furnace gas has the following composition by (volume): N2=60%, H2=4, CO=12%, CO2=24%
(a) if the gas at 298K is burned with the stochiometric amount of dry air at 298 K, what is the composition of the flue gas? What is the adiabatic flame temperature?
(b) repeat the calculation for 30% excess combustion air at 298K
(C)what is the adiabatic flame temperature when the blast furnace gas is preheated to 700K (the dry air is at 298K) (d) suppose the combustion air is not dry ( has partial pressure of water 15 mm Hg and a total pressure of 760 mm Hg) how will thE dlaMe temperature be affected?
Air:n(O2)?0.104n(N2)?0.416DaTA(k J?mol)
FORCOCO2?Hf(kJ/mol) ?110.523
FORCOCO2H2O(g)N2,O2CP[J/mol?K]?? 33575034
?393.513Solution
(a)CO?H2?1212O2?CO2
O2?H2O
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