THERMODYNAMICS(SI UNITS,INTL.ED)EBOOK>I
THERMODYNAMICS(SI UNITS,INTL.ED)EBOOK>I
8th Edition
ISBN: 9781307434316
Author: CENGEL
Publisher: INTER MCG
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Chapter 15.7, Problem 87P
To determine

The entropy generated during the combustion of n-Octane.

The exergy destructed during the combustion of n-Octane.

Expert Solution & Answer
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Answer to Problem 87P

The entropy generated during the combustion of n-Octane is 103.4kJ/Kkg of C8H18.

The exergy destructed during the combustion of n-Octane is 30,805kJ/Kkg of C8H18.

Explanation of Solution

Write the complete balanced reaction for combustion of octane (C3H8) with 70% excess theoretical amount of air.

C8H18+1.7ath(O2+3.76N2)8CO2+9H2O+0.7athO2+(1.7)3.76athN2 (I)

Write the energy balance equation for the combustion of octane (C3H8).

Qout=NP(h¯fo+h¯h¯o)PNR(h¯fo+h¯h¯o)R (II)

Here, the amount of heat transfer for the combustion of octane gas is Qout, number of moles of product is NP, number of moles of reactants is NR, enthalpy of vaporization is h¯fo, enthalpy of formation at a temperature is h¯, and the enthalpy of formation at the standard reference state is h¯o.

Write the formula to calculate the entropy of an i component (Si).

Si=Nis¯i(T,Pi)

Si=Ni[s¯io(T,Po)Ruln(yiPm)] (III)

Here, number of moles of i component is Ni, entropy of the i component is s¯i(T,Pi), entropy of vaporization is s¯io(T,Po), universal gas constant is Ru, mole fraction of i component is yi, and the total pressure is Pm.

Write the formula to calculate the entropy generation (Sgen) for the combustion process.

Sgen=SPSR+QoutTsurr (IV)

Here, entropy of the products is SP, entropy of the reactants is SR, and the temperature of the surroundings is Tsurr.

Write the expression to calculate the entropy generated per unit mass (S¯gen).

S¯gen=SgenMfuel (V)

Here, molar mass of the fuel is Mfuel.

Write the expression to calculate the exergy destructed per unit mass (X¯dest).

X¯dest=ToSgenMfuel (VI)

Here, temperature of surroundings is To.

Conclusion:

Balance for the oxygen from combustion equation (I).

1.7ath=8+4.5+0.7athath=12.5

Rewrite the combustion reaction of propane with 95% theoretical amount of air.

C8H18(l)+1.7(12.5)[O2+3.76N2]{8CO2+9H2O+(1.7×12.5)O2+(1.7×12.5×3.76)N2}

C8H18(l)+21.25[O2+3.76N2]8CO2+9H2O+8.75O2+79.9N2 (VII)

Rewrite the Equation (II) for the heat transfer from combustion.

Qout=NP(h¯f+h¯h¯)P+NR(h¯f+h¯h¯)R={NCO2(h¯f+h¯h¯)CO2+NH2O(h¯f+h¯h¯)H2O+NO2(h¯f+h¯h¯)O2+NN2(h¯f+h¯h¯)N2NC8H18(h¯f+h¯h¯)C8H18NO2(h¯f+h¯h¯)O2NN2(h¯f+h¯h¯)N2} (VIII)

Here, number of moles of product is NP, number of moles of reactants is NR, number of moles of CO2 is NCO2, number of moles of H2O is NH2O, number of moles of O2 is NO2, number of moles of N2 is NN2, number of moles of C8H18 is NC8H18, enthalpy at reference state is h¯f, sensible enthalpy at specified state is h¯, and sensible enthalpy at reference state is h¯.

From the Table A-18 through Table A-26, obtain the enthalpies of vaporization and the enthalpies of formation for different substance as follows,

Substance

h¯f°

kJ/kmol

h¯298K°

kJ/kmol

h¯600K°

kJ/kmol

h¯1340K

kJ/kmol

C8H18(l)249,950000
O20868217,92943,475
N20866917,56341,539
H2O(g)241,8209904050,612
CO2393,5209364061,813

Substitute 8kmol for NCO2, 393,520kJ/kmol for h¯f,CO2°, 9,364kJ/kmol for h¯298K,CO2°, 61,183kJ/kmol for h¯1340K,CO2, 9kmol for NH2O, 241,820kJ/kmol for h¯f,H2O°, 50,612kJ/kmol for h¯1340K,H2O, 9,904kJ/kmol for h¯298K,H2O°, 8.75kmol for NO2, 0 for h¯f,O2°, 8,682kJ/kmol for h¯298K,O2°, 43,475kJ/kmol for h¯1340K,O2, 79.9kmol for NN2, 0 for h¯f,N2°, 8,669kJ/kmol for h¯298K,N2°, 41,539kJ/kmol for h¯1340K,N2, 1kmol for NC8H18, 208,450kJ/kmol for h¯f,C8H18°, 0 for h¯298K,C8H18°, and 0 for h¯600K,C8H18, 21.25kmol for NO2, 17,929kJ/kmol for h¯600K,O2, and 17,563kJ/kmol for h¯600K,N2 in Equation (VIII).

Qout={(8kmol)(393,520kJ/kmol+61,183kJ/kmol9,364kJ/kmol)+(9kmol)(241,820kJ/kmol+50,162kJ/kmol9,904kJ/kmol)+(8.75kmol)(0+43,475kJ/kmol8,682kJ/kmol)+(79.9kmol)(0+41,539kJ/kmol8,669kJ/kmol)(1kmol)(208,450kJ/kmol+00)(21.25kmol)(0+17,929kJ/kmol8,682kJ/kmol)(79.9kmol)(0+17,563kJ/kmol8,669kJ/kmol)}=2,265,004kJ/kmolofC8H18

From the Table A-18 through Table A-26, obtain the entropy values for different substance and tabulate using the Equation (III).

Represent the entropy calculations for the reactants as in Table below.

SubstanceNiyis¯i, (T,1atm)Ruln(yiPm)Nis¯i
C8H18(l)1466.7314.79451.94
O221.250.21226.351.814771.48
N279.90.79212.0712.8315,919.28
Entropy of the reactant, SRSR=21,142.70kJ/K

Represent the entropy calculations for the products as in Table below.

SubstanceNiyis¯i, (T,1atm)Ruln(yiPm)Nis¯i
CO280.0757292.11–6.6732390.26
H2O(g)90.0852250.45–5.6902305.26
O28.750.0828257.97–5.9282309.11
N279.90.7563241.77–12.4618,321.87
Entropy of the product, SPSP=25,326.50kJ/K

Substitute 25,326.50kJ/K for SP, 21,142.70kJ/K for SR, 2,265,004kJ/kmolofC8H18 for Qout, and 298K for Tsurr in Equation (IV).

Sgen=25,326.50kJ/K21,142.70kJ/K+2,265,004kJ/kmolofC8H18298K=11,784.5kJ/Kper kmol ofC8H18

From the table A-2 of “Molar mass, gas constants, and critical-point properties”, select the molar masses of liquid octane as,

Mfuel=114kg/kmol

Substitute 11,784.5kJ/Kkmol for Sgen, and 114kg/kmol for Mfuel in Equation (V).

S¯gen=11,784.5kJ/Kkmol114kg/kmol=103.4kJ/KkgC8H18

Thus, the entropy generated during the combustion of n-Octane is 103.4kJ/Kkg of C8H18.

Substitute 298K for T0, 11,784.5kJ/Kkmol for Sgen, and 114kg/kmol for Mfuel in Equation (VI).

X¯dest=(298K)(11,784.5kJ/Kkmol)114kg/kmol=30,805kJ/KkgC8H18

Thus, the exergy destructed during the combustion of n-Octane is 30,805kJ/Kkg of C8H18.

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Chapter 15 Solutions

THERMODYNAMICS(SI UNITS,INTL.ED)EBOOK>I

Ch. 15.7 - What are the causes of incomplete combustion?Ch. 15.7 - Which is more likely to be found in the products...Ch. 15.7 - Methane (CH4) is burned with the stoichiometric...Ch. 15.7 - Prob. 14PCh. 15.7 - n-Butane fuel (C4H10) is burned with the...Ch. 15.7 - Prob. 16PCh. 15.7 - Prob. 17PCh. 15.7 - 15–18 n-Octane (C8H18) is burned with 50 percent...Ch. 15.7 - In a combustion chamber, ethane (C2H6) is burned...Ch. 15.7 - Prob. 20PCh. 15.7 - Prob. 21PCh. 15.7 - 15–22 One kilogram of butane (C4H10) is burned...Ch. 15.7 - 15–23E One lbm of butane (C4H10) is burned with 25...Ch. 15.7 - Prob. 24PCh. 15.7 - A fuel mixture of 60 percent by mass methane (CH4)...Ch. 15.7 - A certain natural gas has the following volumetric...Ch. 15.7 - Prob. 27PCh. 15.7 - A gaseous fuel with a volumetric analysis of 45...Ch. 15.7 - Prob. 30PCh. 15.7 - 15–31 Octane (C8H18) is burned with dry air. The...Ch. 15.7 - Prob. 32PCh. 15.7 - Prob. 33PCh. 15.7 - Prob. 34PCh. 15.7 - Prob. 35PCh. 15.7 - Prob. 36PCh. 15.7 - Prob. 37PCh. 15.7 - Prob. 38PCh. 15.7 - Prob. 39PCh. 15.7 - Prob. 40PCh. 15.7 - Prob. 41PCh. 15.7 - Prob. 42PCh. 15.7 - Prob. 44PCh. 15.7 - Repeat Prob. 1546 for liquid octane (C8H18).Ch. 15.7 - Ethane (C2H6) is burned at atmospheric pressure...Ch. 15.7 - Reconsider Prob. 1550. What minimum pressure of...Ch. 15.7 - Calculate the HHV and LHV of gaseous n-octane fuel...Ch. 15.7 - Prob. 49PCh. 15.7 - Prob. 50PCh. 15.7 - Consider a complete combustion process during...Ch. 15.7 - Prob. 53PCh. 15.7 - Prob. 54PCh. 15.7 - Propane fuel (C3H8) is burned with an airfuel...Ch. 15.7 - 15–56 Hydrogen (H2) is burned completely with the...Ch. 15.7 - Prob. 57PCh. 15.7 - Prob. 58PCh. 15.7 - Octane gas (C8H18) at 25C is burned steadily with...Ch. 15.7 - Prob. 61PCh. 15.7 - Liquid ethyl alcohol [C2H5OH(l)] at 25C is burned...Ch. 15.7 - Prob. 63PCh. 15.7 - Prob. 64PCh. 15.7 - A constant-volume tank contains a mixture of 120 g...Ch. 15.7 - Prob. 67PCh. 15.7 - Prob. 68PCh. 15.7 - Prob. 69PCh. 15.7 - A fuel is completely burned first with the...Ch. 15.7 - Prob. 71PCh. 15.7 - Acetylene gas (C2H2) at 25C is burned during a...Ch. 15.7 - Octane gas (C8H18) at 25C is burned steadily with...Ch. 15.7 - Express the increase of entropy principle for...Ch. 15.7 - Prob. 81PCh. 15.7 - What does the Gibbs function of formation gf of a...Ch. 15.7 - Liquid octane (C8H18) enters a steady-flow...Ch. 15.7 - Benzene gas (C6H6) at 1 atm and 77F is burned...Ch. 15.7 - Prob. 87PCh. 15.7 - Prob. 88PCh. 15.7 - A steady-flow combustion chamber is supplied with...Ch. 15.7 - Prob. 91RPCh. 15.7 - 15–92 A gaseous fuel with 80 percent CH4, 15...Ch. 15.7 - Prob. 93RPCh. 15.7 - Prob. 94RPCh. 15.7 - Prob. 95RPCh. 15.7 - Prob. 96RPCh. 15.7 - Prob. 97RPCh. 15.7 - Prob. 98RPCh. 15.7 - Prob. 99RPCh. 15.7 - Prob. 100RPCh. 15.7 - A 6-m3 rigid tank initially contains a mixture of...Ch. 15.7 - Prob. 102RPCh. 15.7 - Propane gas (C3H8) enters a steady-flow combustion...Ch. 15.7 - Determine the highest possible temperature that...Ch. 15.7 - Prob. 106RPCh. 15.7 - Prob. 107RPCh. 15.7 - A steam boiler heats liquid water at 200C to...Ch. 15.7 - Repeat Prob. 15112 using a coal from Utah that has...Ch. 15.7 - Liquid octane (C8H18) enters a steady-flow...Ch. 15.7 - Prob. 111RPCh. 15.7 - Prob. 112RPCh. 15.7 - Prob. 113RPCh. 15.7 - Consider the combustion of a mixture of an...Ch. 15.7 - A fuel is burned steadily in a combustion chamber....Ch. 15.7 - A fuel is burned with 70 percent theoretical air....Ch. 15.7 - Prob. 123FEPCh. 15.7 - One kmol of methane (CH4) is burned with an...Ch. 15.7 - An equimolar mixture of carbon dioxide and water...Ch. 15.7 - The higher heating value of a hydrocarbon fuel...Ch. 15.7 - Acetylene gas (C2H2) is burned completely during a...Ch. 15.7 - Prob. 129FEPCh. 15.7 - A fuel is burned during a steady-flow combustion...
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What is entropy? - Jeff Phillips; Author: TED-Ed;https://www.youtube.com/watch?v=YM-uykVfq_E;License: Standard youtube license