Thermodynamics: An Engineering Approach
Thermodynamics: An Engineering Approach
8th Edition
ISBN: 9780073398174
Author: Yunus A. Cengel Dr., Michael A. Boles
Publisher: McGraw-Hill Education
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Chapter 13.3, Problem 91RP

a)

To determine

The total entropy change and exergy destruction associated with the process using ideal gas approximation.

a)

Expert Solution
Check Mark

Answer to Problem 91RP

The entropy generated is 1.61kJ/kmolK.

The energy destroyed is 488kJ/kmol.

Explanation of Solution

Write the entropy balance equation to obtain the expression of entropy generation in terms of O2andN2.

SinSout+Sgen=ΔSsystemQinTb,surr+Sgen=m(s2s1)Sgen=m(s2s1)+QinTsurrSgen=mO2(s2s1)O2+mN2(s2s1)N2QinTsurr (I)

Here, mass of O2 is mO2, mass of N2 is mN2, boundary temperature is Tb,surr, surrounding temperature is Tsurr, entropy at state 1 and 2 is s1ands2, entropy generation is Sgen, heat input is Qin, outlet entropy is Sout, and inlet entropy is Sin.

Write the expression to obtain the energy destroyed during a process (Xdestroyed).

Xdestroyed=T0Sgen (II)

Here, initial temperature is T0.

Conclusion:

Refer Table A-2b, “Ideal gas specific heats of various common gases”, obtain the specific heat at constant pressure of O2andN2 at 210K and 180K as 0.918kJ/kgK, and 1.039kJ/kgK respectively.

Obtain the value of (s2s1)O2 from Equation (I).

(s2s1)O2=(cplnT2T1RlnP20P1)O2 (III)

Here, constant pressure specific heat is cp, initial temperature and pressure is T1andP1, and apparent gas constant is R.

The partial pressure of O2 gas remains constant in the total mixture pressure, thus calculate (s2s1)O2 from Equation (III).

(s2s1)O2=(cplnT2T1)O2 (IV)

Substitute 0.918kJ/kgK for cp, 210 K for T2, and 180 K for T1 in Equation (IV).

(s2s1)O2=((0.918kJ/kgK)ln210K180K)=0.141kJ/kgK

Obtain the value of (s2s1)N2 from Equation (I).

(s2s1)N2=(cplnT2T1RlnP20P1)N2 (V)

The partial pressure of N2 gas remains constant in the total mixture pressure, thus calculate (s2s1)N2 from Equation (V).

(s2s1)N2=(cplnT2T1)N2 (VI)

Substitute 1.039kJ/kgK for cp, 210 K for T2, 180 K for T1 in Equation (VI).

(s2s1)N2=((1.039kJ/kgK)ln210K180K)=0.160kJ/kgK

Substitute 32kg/kmol for mO2, 28kg/kmol for mN2, 0.141kJ/kgK for (s2s1)H2, 0.160kJ/kgK for (s2s1)N2, 872 kJ for Qin, and 303 K for Tsurr in Equation (I).

Sgen=[(32kg/kmol)(0.141kJ/kgK)+(28kg/kmol)(0.160kJ/kgK)872kJ303K]=1.61kJ/kmolK

Thus, the entropy generated is 1.61kJ/kmolK.

Substitute 303 K for T0 and 1.61kJ/kmolK for Sgen in Equation (II).

Xdestroyed=(303K)(1.61kJ/kmolK)=488kJ/kmol

Thus, the energy destroyed is 488kJ/kmol.

b)

To determine

The total entropy change and exergy destruction associated with the process using Kay’s rule.

b)

Expert Solution
Check Mark

Answer to Problem 91RP

The entropy generation is 3.41kJ/kmolK.

The energy destroyed is 1,034kJ/kmol.

Explanation of Solution

Write the expression to obtain the pseudo-critical temperature of the mixture (Tcr,m).

Tcr,m=yiTcr,i=yO2Tcr,O2+yN2Tcr,N2 (VII)

Here, mole fraction of O2,andN2 is yO2andyN2 and critical temperature of O2,andN2 are Tcr,O2,andTcr,N2.

Write the expression to obtain the pseudo-critical pressure of the mixture (Pcr,m).

Pcr,m=yiPcr,i=yO2Pcr,O2+yN2Pcr,N2 (VIII)

Here, critical pressure of O2,andN2 are Pcr,O2,andPcr,N2.

Write the expression to obtain the initial reduced temperature (TR,1).

TR,1=Tm.1Tcr,m (IX)

Here, mixing critical temperature is Tcr,m.

Write the expression to obtain the initial reduced pressure (PR,1).

PR,1=PR,2=PmPcr,m (X)

Here, mixing critical pressure is Pcr,m.

Write the expression to obtain the final reduced temperature (TR,2).

TR,2=Tm,2Tcr,m (XI)

Write the expression to obtain the specific change in entropy of a system (Δs¯sys).

Δs¯sys=Ru(Zs1Zs2)+(Δs¯sys,ideal) (XII)

Here, universal gas constant is Ru.

Write the expression to obtain the entropy generation (Sgen).

Sgen=Δs¯sysQinTsurr (XIII)

Write the expression to obtain the energy destroyed during a process (Xdestroyed).

Xdestroyed=T0Sgen (XIV)

Here, initial temperature is T0.

Conclusion:

From the Table of critical properties, obtain the critical temperature and pressure for O2 as 154.8 K and 5.08 MPa and critical temperature and pressure for N2 as 126.2 K and 3.39 MPa.

Substitute 0.25 for yO2, 154.8 K for Tcr,O2, 0.75 for yN2, and 126.2 K for Tcr,N2 in Equation (VII).

Tcr,m=0.25(154.8K)+0.75(126.2K)=133.4K

Substitute 0.25 for yO2, 5.08 MPa for Pcr,O2, 0.75 for yN2, and 3.39 MPa for Pcr,N2 in Equation (VIII).

Pcr,m=0.25(5.08MPa)+0.75(3.39MPa)=3.81MPa

Substitute 180 K for Tm,1 and 133.4 K for Tcr,m in Equation (IX).

TR,1=180K133.4K=1.349

Substitute 8 MPa for Pm and 3.81 MPa for Pcr,m in Equation (X).

PR,1=8MPa3.81MPa=2.1

Refer Figure A-30, “Generalized entropy departure chart”, obtain the value of initial entropy departure (Zs2) as 0.8 by taking PR,1 as 2.1 and TR,1 as 1.349.

Substitute 210 K for Tm,2 and 133.4 K for Tcr,m in Equation (XI).

TR,2=210K133.4K=1.574

Refer Figure A-30, “Generalized entropy departure chart”, obtain the value of final entropy departure (Zs2) as 0.45 by taking PR,2 as 2.1 and TR,2 as 1.574.

Substitute 8.314kJ/kmolK for Ru, 0.8 for Zs1, 0.45 for Zs2, and 4.49kJ/kmolK for Δs¯sys,ideal in Equation (XII).

Δs¯sys=8.314kJ/kmolK(0.80.45)+4.49kJ/kmolK=7.40kJ/kmolK

Substitute 7.40kJ/kmolK for Δs¯sys, 1,204.7kJ/kmol for Qin, and 303K for Tsurr in Equation (XIII).

Sgen=7.40kJ/kmolK1,204.7kJ/kmol303K=3.41kJ/kmolK

Thus, the entropy generation is 3.41kJ/kmolK.

Substitute 303 K for T0 and 3.41kJ/kmolK for Sgen in Equation (XIV).

Xdestroyed=(303K)(3.41kJ/kmolK)=1,034kJ/kmol

Thus, the energy destroyed is 1,034kJ/kmol.

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Chapter 13 Solutions

Thermodynamics: An Engineering Approach

Ch. 13.3 - Prob. 11PCh. 13.3 - Prob. 12PCh. 13.3 - Prob. 13PCh. 13.3 - Is a mixture of ideal gases also an ideal gas?...Ch. 13.3 - Express Daltons law of additive pressures. Does...Ch. 13.3 - Express Amagats law of additive volumes. Does this...Ch. 13.3 - How is the P-v-T behavior of a component in an...Ch. 13.3 - Prob. 18PCh. 13.3 - Prob. 19PCh. 13.3 - Prob. 20PCh. 13.3 - Prob. 21PCh. 13.3 - Consider a rigid tank that contains a mixture of...Ch. 13.3 - Is this statement correct? The volume of an...Ch. 13.3 - Is this statement correct? The temperature of an...Ch. 13.3 - Is this statement correct? The pressure of an...Ch. 13.3 - Prob. 26PCh. 13.3 - Prob. 27PCh. 13.3 - Prob. 28PCh. 13.3 - 13–29 A gas mixture at 350 K and 300 kPa has the...Ch. 13.3 - Prob. 30PCh. 13.3 - Prob. 31PCh. 13.3 - A rigid tank that contains 2 kg of N2 at 25C and...Ch. 13.3 - Prob. 33PCh. 13.3 - Prob. 34PCh. 13.3 - Prob. 35PCh. 13.3 - Prob. 36PCh. 13.3 - A 30 percent (by mass) ethane and 70 percent...Ch. 13.3 - Prob. 38PCh. 13.3 - Prob. 39PCh. 13.3 - Prob. 40PCh. 13.3 - Prob. 41PCh. 13.3 - Prob. 42PCh. 13.3 - Prob. 43PCh. 13.3 - Is the total internal energy of an ideal-gas...Ch. 13.3 - Prob. 45PCh. 13.3 - Prob. 46PCh. 13.3 - 13–47C Is the total internal energy change of an...Ch. 13.3 - Prob. 48PCh. 13.3 - Prob. 49PCh. 13.3 - The volumetric analysis of a mixture of gases is...Ch. 13.3 - Prob. 52PCh. 13.3 - Prob. 53PCh. 13.3 - Prob. 54PCh. 13.3 - Prob. 55PCh. 13.3 - Prob. 56PCh. 13.3 - An insulated tank that contains 1 kg of O2at 15C...Ch. 13.3 - Prob. 59PCh. 13.3 - Prob. 60PCh. 13.3 - Prob. 61PCh. 13.3 - Prob. 62PCh. 13.3 - Prob. 63PCh. 13.3 - Prob. 64PCh. 13.3 - Prob. 66PCh. 13.3 - Prob. 67PCh. 13.3 - Prob. 69PCh. 13.3 - A pistoncylinder device contains 6 kg of H2 and 21...Ch. 13.3 - Prob. 71PCh. 13.3 - Prob. 72PCh. 13.3 - Prob. 73PCh. 13.3 - Prob. 74PCh. 13.3 - Prob. 75PCh. 13.3 - Prob. 76PCh. 13.3 - Prob. 77PCh. 13.3 - Prob. 78PCh. 13.3 - Prob. 80PCh. 13.3 - Prob. 81PCh. 13.3 - Fresh water is obtained from seawater at a rate of...Ch. 13.3 - Prob. 83PCh. 13.3 - Prob. 84RPCh. 13.3 - The products of combustion of a hydrocarbon fuel...Ch. 13.3 - Prob. 89RPCh. 13.3 - Prob. 91RPCh. 13.3 - Prob. 92RPCh. 13.3 - A spring-loaded pistoncylinder device contains a...Ch. 13.3 - Prob. 94RPCh. 13.3 - Reconsider Prob. 1395. Calculate the total work...Ch. 13.3 - A rigid tank contains a mixture of 4 kg of He and...Ch. 13.3 - Prob. 97RPCh. 13.3 - Prob. 100RPCh. 13.3 - An ideal-gas mixture whose apparent molar mass is...Ch. 13.3 - 13–102 An ideal-gas mixture consists of 2 kmol of...Ch. 13.3 - An ideal-gas mixture consists of 2 kmol of N2and 4...Ch. 13.3 - Prob. 104FEPCh. 13.3 - Prob. 105FEPCh. 13.3 - An ideal-gas mixture consists of 3 kg of Ar and 6...Ch. 13.3 - Prob. 107FEPCh. 13.3 - Prob. 108FEPCh. 13.3 - Prob. 109FEPCh. 13.3 - Prob. 110FEP
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