The second law efficiency and the exergy destruction during the expansion process.
Answer to Problem 97RP
The second law efficiency is 89.4%.
The exergy destruction during the expansion process is 79 kJ/kg.
Explanation of Solution
Write the expression to obtain the mole number of O2 (NO2).
NO2=mO2MO2 (I)
Here, molar mass of O2 is MO2 and mass of O2 is mO2.
Write the expression to obtain the mole number of CO2 (NCO2).
NCO2=mCO2MCO2 (II)
Here, molar mass of CO2 is MCO2 and mass of CO2 is mCO2.
Write the expression to obtain the mole number of He (NHe).
NHe=mHeMHe (III)
Here, molar mass of He is MHe and mass of He is mHe.
Write the expression to obtain the mass fraction of O2 (mfO2).
mfO2=mO2mm (IV)
Write the expression to obtain the mass fraction of CO2 (mfCO2).
mfCO2=mCO2mm (V)
Write the expression to obtain the mass fraction of He (mfHe).
mfHe=mHemm (VI)
Write the expression to obtain the equation to calculate the mole number of the mixture (Nm).
Nm=NN2+NHe+NCH4+NC2H6 (VII)
Write the expression to obtain the molar mass of the gas mixture (Mm).
Mm=mmNm (VIII)
Write the expression to obtain the equation to calculate the constant-pressure specific heat of the mixture (cp).
cp=mfO2cp,O2+mfCO2cp,CO2+mfHecp,He (IX)
Here, constant pressure specific heat of O2, He, and CO2 are cp,O2, cp,He, and cp,CO2 respectively.
Write the expression to obtain the gas constant of the mixture (R).
R=RuMm (X)
Here, the universal gas constant is Ru.
Write the expression to obtain the constant volume specific heat (cv).
cv=cp−R (XI)
Write the expression to obtain the specific heat ratio (k).
k=cpcv (XII)
Write the expression to obtain the temperature at the end of the expansion for the isentropic process (T2s).
T2s=T1(P2P1)(k−1)/k (XIII)
Write the expression to obtain the actual outlet temperature (T2).
T2=T1−ηturb(T1−T2s) (XIV)
Here, efficiency of the turbine is ηturb.
Write the expression to obtain the entropy change of the gas mixture (s2−s1).
s2−s1=cplnT2T1−RlnP2P1 (XV)
Write the expression to obtain the actual work output (wout).
wout=cp(T1−T2) (XVI)
Write the expression to obtain the reversible work output (wrev,out).
wrev,out=wout−T0(s1−s2) (XVII)
Write the expression to obtain the second law efficiency (ηII).
ηII=woutwrev,out (XVIII)
Write the expression to obtain the exergy destruction (xdest).
xdest=wrev,out−wout (XIX)
Conclusion:
Refer Table A-1, “Molar mass, gas constant, and critical point properties”, obtain the molar masses of O2, CO2 and He as 32 kg/kmol, 44 kg/kmol and 4 kg/kmol respectively.
Substitute 0.1 kg for mN2 and 32 kg/kmol for MO2 in Equation (I).
NO2=0.1 kg32 kg/kmol=0.003125 kmol
Substitute 1 kg for mCO2 and 44 kg/kmol for MCO2 in Equation (II).
NCO2=1 kg(44 kg/kmol)=0.02273 kmol
Substitute 0.5 kg for mHe and 4 kg/kmol for MHe in Equation (III).
NHe=0.5 lbm(4 kg/kmol)=0.125 kmol
Substitute 0.003125 kmol for NO2, 0.02273 kmol for NCO2 and 0.125 kmol for NHe in Equation (VII).
Nm=0.003125 kmol+0.02273 kmol+0.125 kmol=0.15086 kmol
Substitute 1.6 kg for mm and 0.15086 kmol for Nm in Equation (X).
Mm=1.6 kg0.15086 kmol=10.61 kg/kmol
Substitute 8.314 kJ/Kmol⋅K for Ru and 10.61 kg/kmol for Mm in Equation (IX).
R=8.314 kJ/Kmol⋅K10.61 kg/kmol=0.7836 kJ/kg⋅K
Substitute 0.1 kg for mO2 and 1.6 kg for mm in Equation (IV).
mfO2=0.1 kg1.6 kg=0.0625
Substitute 1 kg for mCO2 and 1.6 kg for mm in Equation (V).
mfCO2=1 kg1.6 kg=0.625
Substitute 0.5 kg for mHe and 1.6 kg for mm in Equation (VI).
mfHe=0.5 kg1.6 kg=0.3125
Refer Table A-2a, “Ideal gas specific heats of various common gases”, obtain the constant pressure specific heats of O2, He and CO2 as 0.918 kJ/kg⋅K, 5.1926 kJ/kg⋅K, and 0.846 kJ/kg⋅K.
Substitute 0.0625 for mfO2, 0.625 for mfCO2, 0.3125 for mfHe, 0.918 kJ/kg⋅K for cp,O2, 5.1926 kJ/kg⋅K for cp,He, and 0.846 kJ/kg⋅K for cp,CO2 in Equation (IX).
cp=[(0.0625)(0.918 kJ/kg⋅K)+(0.625)(0.846 kJ/kg⋅K)++(0.3125)(5.1926 kJ/kg⋅K)]=2.209 kJ/kg⋅K
Substitute 0.7836 kJ/kg⋅K for R and 2.209 kJ/kg⋅K for cp in Equation (XI).
cv=2.209 kJ/kg⋅K−0.7836 kJ/kg⋅K=1.425 kJ/kg⋅K
Substitute 2.209 kJ/kg⋅K for cp and 1.425 kJ/kg⋅K for cv in Equation (XII).
k=2.209 kJ/kg⋅K1.425 kJ/kg⋅K=1.550
Substitute 1.550 for k, 327°C for T1, 100 kPa for P2, and 1000 kPa for P1 in Equation (XIII).
T2s=(327°C)(100 kPa1000 kPa)(1.550−1)/1.550=(327+273)K(100 kPa1000 kPa)(1.550−1)/1.550=265 K
Substitute 327°C for T1, 265 K for T2s and 0.90 for ηturb in Equation (XIV).
T2=327°C−0.90(327°C−265 K)=(327+273)K−0.90((327+273)K−265 K)=299 K
Substitute 2.209 kJ/kg⋅K for cp, 299 K for T2, 327°C for T1, 0.7836 kJ/kg⋅K for R, 100 kPa for P2, and 1000 kPa for P1 in Equation (XV).
s2−s1={(2.209 kJ/kg⋅K)ln(299 K327°C)−(0.7836 kJ/kg⋅K)ln(100 kPa1000 kPa)}={(2.209 kJ/kg⋅K)ln(299 K(327+273)K)−(0.7836 kJ/kg⋅K)ln(100 kPa1000 kPa)}=0.2658 kJ/kg⋅K
Substitute 2.209 kJ/kg⋅K for cp, 299 K for T2 and 327°C for T1 in Equation (XVI).
wout=2.209 kJ/kg⋅K(327°C−299 K)=2.209 kJ/kg⋅K((327+273)K−299 K)=665 kJ/kg
Substitute 665 kJ/kg for wout, 25°C for T0 and (−0.2658 kJ/kg⋅K) for (s1−s2) in Equation (XVII).
wrev,out=665 kJ/kg−25°C(0.2658 kJ/kg⋅K)=665 kJ/kg−(25+273)K×(−0.2658 kJ/kg⋅K)=744 kJ/kg
Substitute 665 kJ/kg for wout and 744 kJ/kg for wrev,out in Equation (XVIII).
ηII=665 kJ/kg744 kJ/kg=0.894×100%=89.4%
Thus, the second law efficiency is 89.4%.
Substitute 665 kJ/kg for wout and 744 kJ/kg for wrev,out in Equation (XIX).
xdest=744 kJ/kg−665 kJ/kg=79 kJ/kg
Thus, the exergy destruction during the expansion process is 79 kJ/kg.
Want to see more full solutions like this?
Chapter 13 Solutions
Thermodynamics: An Engineering Approach
- Mych CD 36280 kg. 0.36 givens Tesla truck frailer 2017 Model Vven 96154kph ronge 804,5km Cr Powertrain Across PHVAC rwheel 0.006 0.88 9M² 2 2kW 0.55M ng Zg Prated Trated Pair 20 0.95 1080 kW 1760 Nm 1,2 determine the battery energy required to meet the range when fully loaded determine the approximate time for the fully-loaded truck-trailor to accelerate from 0 to 60 mph while Ignoring vehicle load forcesarrow_forward12-217. The block B is sus- pended from a cable that is at- tached to the block at E, wraps around three pulleys, and is tied to the back of a truck. If the truck starts from rest when ID is zero, and moves forward with a constant acceleration of ap = 0.5 m/s², determine the speed of the block at D the instant x = 2 m. Neglect the size of the pulleys in the calcu- lation. When xƊ = 0, yc = 5 m, so that points C and D are at the Prob. 12-217 5 m yc =2M Xparrow_forwardsolve both and show matlab code auto controlsarrow_forward
- 12-82. The roller coaster car trav- els down the helical path at con- stant speed such that the paramet- ric equations that define its posi- tion are x = c sin kt, y = c cos kt, z = h - bt, where c, h, and b are constants. Determine the mag- nitudes of its velocity and accelera- tion. Prob. 12-82 Narrow_forwardGiven: = refueling Powertran SOURCE EMISSIONS vehide eff eff gasoline 266g co₂/kwh- HEV 0.90 0.285 FLgrid 411ilg Co₂/kWh 41111gCo₂/kWh EV 0.85 0.80 Production 11x10% og CO₂ 13.7 x 10°g CO₂ A) Calculate the breakeven pont (in km driven) for a EV against on HEV in Florida of 0.1kWh/kM Use a drive cycle conversion 5) How efficient would the powertrain of the HEV in this example have to be to break even with an EV in Florida after 150,000 Miles of service (240,000) km Is it plausible to achieve the answer from pert b Consideans the HaXINERY theoretical efficiency of the Carnot cycle is 5020 and there are additional losses of the transMISSION :- 90% efficiency ? c A what do you conclude is the leading factor in why EVs are less emissive than ICE,arrow_forwardsolve autocontrolsarrow_forward
- Problem 3.21P: Air at 100F(38C) db,65F(18C) wb, and sea-level pressure is humidified adiabatically with steam. The steam supplied contains 20 percent moisture(quality of 0.80) at 14.7psia(101.3kpa). The air is humidified to 60 percent relative humidity. Find the dry bulb temperature of the humidified air using (a)chart 1a or 1b and (b) the program PSYCH.arrow_forwardPUNTO 4. calculate their DoF using Gruebler's formula. PUNTO 5. Groundarrow_forwardPUNTO 2. PUNTO 3. calculate their DoF using Gruebler's formula. III IAarrow_forward
- calculate their DoF using Gruebler's formula. PUNTO 6. PUNTO 7. (Ctrl)arrow_forwardA pump delivering 230 lps of water at 30C has a 300-mm diameter suction pipe and a 254-mm diameter discharge pipe as shown in the figure. The suction pipe is 3.5 m long and the discharge pipe is 23 m long, both pipe's materials are cast iron. The water is delivered 16m above the intake water level. Considering head losses in fittings, valves, and major head loss. a) Find the total dynamic head which the pump must supply. b)It the pump mechanical efficiency is 68%, and the motor efficiency is 90%, determine the power rating of the motor in hp.given that: summation of K gate valve = 0.25check valve=390 degree elbow= 0.75foot valve= 0.78arrow_forwardA pump delivering 230 lps of water at 30C has a 300-mm diameter suction pipe and a 254-mm diameter discharge pipe as shown in the figure. The suction pipe is 3.5 m long and the discharge pipe is 23 m long, both pipe's materials are cast iron. The water is delivered 16m above the intake water level. Considering head losses in fittings, valves, and major head loss. a) Find the total dynamic head which the pump must supply. b)It the pump mechanical efficiency is 68%, and the motor efficiency is 90%, determine the power rating of the motor in hp.arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY