che 302 thermodynamics illlee/f18_qfe4.pdf · quiz 1. carnot efficiency 1 • in a carnot engine,...

Che 3021Thermodynamics I

QUIZZES

RIEPJCPIγPJEJJJY

QUIZ 1. Find Molecular Weights:1

• 1… CO2

• 2…NaCl• 3… Aspirin C9H8O4

CO2 =

NaCl =

C9H8O4 =

PIgPJC

Quiz 1. Temperature conversion1

• Convert 94oF, to • (a). Rankine, oR• (b). Kelvin, K• (c).. Celsius, oC

(a). Rankine, oR = (b). Kelvin, K = (c).. Celsius, oC =

PIgPJC

Quiz 1. Carnot Efficiency1

• In a Carnot engine, the high temperature is 975 oC, and low temperature is 20 oC; what is its thermal efficiency, η?

η =

PIgPJC

Quiz 2. PV Expansion workof ideal gas: PV = nRT

PJE 2• For an ideal gas of 0.7 gmol in a cylinder initially at v1= 5liters and P1= 5 atm. What is its temperature T1 (K)? Expansion at constant temperature takes place until v2 = 10 liters. What is the final pressure P2 (atm)? What work has been done, W (in J)?

• Hints: Find the gas constant, R PJE

T1 =

P2 =

W =

Quiz 2. Ideal gas calculations: PJE 2

• Calculate the volume (in liter) of air (assuming ideal gas, i.e. PV=nRT) at T= 70oF, and P = 1 atm for one lbmol.

• Calculate the temperature of nitrogen (ideal gas) at 20 psia and 102 cuft/lbmol.

• Calculate the specific volume (m3/kmol) of CO2 (ideal gas) at 0.012 bar and -195oF.

Piston-Cylinder Heat Transferpas donne’ PJE 2

• Air is contained in a vertical piston–cylinder assembly by a piston of mass 50 kg and having a face area of 0.01 m2. The mass of the air is 5 g, and initially the air occupies a volume of 5 liters. The atmosphere exerts a pressure of 100 kPa on the top of the piston. The volume of the air slowly decreases to 0.002 m3 as the specific internal energy of the air decreases by 260 kJ/kg. Neglecting friction between the piston and the cylinder wall, determine the heat transfer to the air, in kJ. OJG

Quiz 3. Read Steam Tables & Mollier Charts For water PJJ-3

• (ST) Find the enthalpy (kJ/kg) and internal energy (kJ/kg), and specific volume (m3/kg) for steam at (a) T = 120 oC and P = 1bar, and (b) T = 440 oC and P = 320 bar.

• (MC) Find the enthalpy (Btu/lbm) and entropy (Btu/(lbm,oR) for steam at (a) T = 800 oF and P = 100 psia, and (b) T = 450 oF and P = 60 psia.

QUIZ 3. Read Steam Tablesand Mollier Chart

PJJ-3

• Find specific volume (m3/kg) and enthalpy (kJ/kg) for Steam at T= 520 oC and P= 200 bar.

• T.A-5

• Find the enthalpy, H, from the Mollier chart at T= 700oF, and P=60 psia.

QUIZ 3. Read Steam Tables:PJJ-3

• Find specific volume (m3/kg) and enthalpy (kJ/kg) for subcooled liquid water at T= 200 oC and P= 25 bar.

• T.A-5

• At T= 50 oC, what is the saturate pressure (bar)? What are the saturated liquid and vapor volumes (m3/kg). T.A-2

• At P= 4 bar, what is the saturate temperature (oC)? What are the saturated liquid and vapor volumes (m3/kg). T.A-3

Quiz 4. (1) Ideal gas calculations: RIN

• Given a classroom of size: 25’x30’ x12’, find the air mass (in lbm) at T = 75oF and P= 14.7 psia. PV = nRT. (Choose the right value of R). Air’s average MW is 28.8.

• (2) Use steam tables:

• What is the specific volume (in m3/kg) of water at saturated pressure of 7.85 psia.

• 664.15 lbm

QUIZ 5. Calculate the Heat Capacity, Cp, of nitrogen at T =298 KRIQ• (1) Use the text formula for N2.

•

(2) Use the API formula for N2 .

For N2: Cp* in cal/(gmol.K)B=6.95808, C=2.03952, D= 1681.60, E=5.95648, , F=6535.68

For N2: Cp/R = α + βT + γT2 + δT 3 + εT 4.α= 3.675.β= -1.208e-3.γ= 2.324e-6.δ= -0.632e-9.ε= -0.226e-12

QUIZ #1. OAKRKb11.98

• Find the pressure (atm) of a mixture of • CH4 (0. 5 lbmol) + n-C3H8 (0.5 lbmol) • at T=194°F and V= 7.65 ft3. • Use the van der Waals EOS.

• Table A-24E. (R= 0.7302 atm.ft3 /(lbmol.oR))

CH4 n-C3H8

a 581 2369 atm.(ft3/lbmol)^2

b 0.685 1.444 ft3/lbmol

Ans. 11.98 RKb

• .a= 1323.9• .b= 1.065• T= 194+459.67 = 653.67 oR• P=49.9 atm

QUIZ #2 OAK

• Find the pressure of a mixture of • CH4 (0.18 kmol) + n-C4H10 (0.274 kmol) • at T=238°C and V= 0.241 m3. • Use the Redlich-Kwong EOS.

• (R=0.08314 bar.m3/kmol.K)

CH4 nC4H10

a 32.11 289.5513

b 0.02965 0.0806

QUIZ 5. Calculate the Heat Capacity, Cp, of nitrogen at T =298 KRIQ

• (1) Use the text formula for N2.

•

• (2) Use the API formula for N2 .For N2: Cp* in cal/(gmol.K)B=6.95808, C=2.03952, D= 1681.60, E=5.95648

For N2: Cp/R.α= 3.675.β= -1.208e-3.γ= 2.324e-6.δ= -0.632e-9.ε= -0.226e-12

QUIZ 5. Calculate the enthalpy of steamPJM-4

• For 1 kg of steam at P = 15 bar, and T = 280 oC, the specific volume v = 0.167 m3/kg. The internal energy is u= 2748.6 kJ/kg. Use the formula (Definition) of enthalpy to calculate

• H = U + PV

• What is this H-value (kJ)?• 2999.1 kJ

QUIZ 5. Calculate the enthalpy of steamRIQ

• H = U + PV

• What is this H-value (kJ)?• 2999.1 kJ

PJQ-5QUIZ 6.

QUIZ 4. Use generalized compressibility chart for nitrogen

PJM-4

• For 1 kmol of nitrogen (N2) at P = 35 bar, and T = 280 oC, what is its compressibility, Z?

• Use Figure A1 or A2 in the appendix.

Z = 1.05

QUIZ 7.

• Applying the Maxwell Relations•• Evaluate the partial derivative (∂T/∂v)H for van

der Waals equation in terms of P,v,T, Cp, Cv, and their derivatives. Using the RABbit rule and the Maxwell relations.

RIXPJT

QUIZ 6.

• Applying the Maxwell Relations•• Evaluate the partial derivative (∂s/∂P)T (in

J/(bar.K)) for water vapor at a state fixed by a temperature of 240°C and a specific volume of 0.4646 m3/kg. Use the Redlich–Kwongequation of state and an appropriate Maxwellrelation.

PJT

QUIZ 6.

Quiz 7.9-24-18 F18

• Express the derivative• [∂T/∂V]H

• [∂H/∂T]v

• in terms of P,V,T,Cp,Cv and their derivatives.

• Use Maxwell and other derivative relations• Plus dH = TdS + VdP

Quiz 8.9-26-18 F18

• Express the derivatives• [∂T/∂V]S

• [∂H/∂T]v

• in terms of P,V,T,Cp,Cv and their derivatives.

• Use Maxwell and other derivative relations• Plus dH = TdS + VdP

Quiz 9.10-3-18 F18

• Use graphical differentiation and Clapeyron eq. to find the heat of vaporization of saturated steam at 120oC.

• Given the vapor pressure curve of steam.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140

Steam

T,C VP

QUIZ 7. Find the heat of vaporization (kJ/kg) by the Clausius-Claperon equation at 220oC from the vapor pressures using graphical differentiation.

QUIZ 7. Find the heat of vaporization (kJ/kg) by the Clausius-Claperon equation at 140oC from the vapor pressures using graphical differentiation.

QUIZ 10.

• Find the velocity of sound in air (in ft/s) at • - 40oF (below 0oF) using the ideal gas

equation Pv = RT. • Use k = 1.4.

RJEPJZ

Example: Velocity of Sound in Air

Quiz 11. Change in entropy, ΔS• 10 kmol of Ethylene (C2H4) is

compressed from 1 bar to 100 bar at constant T= 400K. Find its entropy change in (kJ/K). Use the Redlich-Kwong equation.

ΔS = S2-S1 =

RJH

4.2

Quiz 11. Turbine Work outputWinnick <133> PKG+PKH

• Steam at 1000oF and 1000 psia is fed steadily to an adiabatic turbine (Q=0) at a rate of 125 lb/min. If the outlet steam is 450oF and 100 psia, what is the work output in (Btu/min, and kW). (Negligible PE and KE changes).

• Note that 1 Btu/min = 17.58 watts.

Q11: AnsWinnick <133> PKG

• 553.2 kW• 31463 Btu/min

QUIZ 12: Pump

Heat capacity:

C= 1 Btu/(lb*ΔoF)

QUIZ 12 (continued)

QUIZ 13. Carnot Efficiency• In a Carnot engine, the high

temperature is 975 oC, and low temperature is 20 oC; what is its thermal efficiency, η?

• If the Qc = - 23500 kJ, what is the net entropy change (in kJ/K) due to heat transfers QH and Qc in the Cycle?

• Calculate the work produced in this cycle: Wnet =? η = 76.5 %

RJSPIg

QUIZ 14. Entropy change for Id.g.

• An ideal gas is compressed from • T1=300 K, v1 = 10 m3/kg to • T2 = 400 K, v2 = 2 m3/kg. • Find the Δs in (kJ/(kg.K). • Constant heat capacity is assumed at

Cv=1.008 kJ/(kg.K).

RJSPIg

QUIZ 15: Hot/Cold Isentropic Processes:

• (1) T1= 230K, P1=100 bar, • T2= 350K, find P2? • (a) Use Isentropy (Cold):• P2/P1 =• (b) Use Tables (A22) (Hot):• Pr2= ?, Pr1=?• P2= P1*(Pr2/Pr1)=

Quiz 15b Using Cold & Hot ProcessesRJZPKN <451> Otto

• In a compressor, air goes through an adiabatic and reversible compression from P1= 1 atm, and V1 = 0.2 cuft to V2=0.025 cuft at T1 = 540 oR. The hat capacity ratio k= Cp/Cv=1.4.

• (a) Use the “cold” equations to find T2 (oR), and P2 (atm).

• (b) Use table A-22E (the “hot” process) to find T2 (oR), and P2 (atm). (Interpolate if needed!)

QUIZ 16: Hot/Cold Isentropic Processes:

• (1) T1= 230K, P1=100 bar, • T2= 350K, find P2? • (a) Use Isentropy (Cold):• P2/P1 =• (b) Use Tables (A22) (Hot):• Pr2= ?, Pr1=?• P2= P1*(Pr2/Pr1)=

QUIZ 17: Otto Cycle (Hot)for unit mass (1 kg of working fluid) flowing through.Heat addition QH is 1400 kJ/kg during combustion.

• (a) Compression Stroke (1-2):• T1= 300K, P1=1 bar, r=8.5• (b) Find T2(K), u2(kJ/kg) from Table A-22.• (c) Use 1st law for “Combust (2-3)”:• m(u3-u2) = QH +0• find u3 and T3! (interpolate!)

8.5

Vr1, Vr2,V2

QUIZ 18: Otto Cycle (Cold)for unit mass (1 kg of working fluid) flowing through.Heat addition QH is 1400 kJ/kg during combustion.

• (a) Compression Stroke (1-2):• T1= 300K, P1=1 bar, r=8.5• (b) Find T2(K) & “u2(kJ/kg) =Cv*T2”• (c) Use 1st law for “Combustion (2-3)”:• m(u3-u2) = QH +0• find u3 =Cv*T3 (kJ/kg). • Use k=1.4!• Cv=0.713 (kJ/(kg.ΔKelvin))

8.5

QUIZ #19. OAKRKb11.98

• Find the pressure (atm) of a mixture of • CH4 (0. 5 lbmol) + n-C3H8 (0.5 lbmol) • at T=194°F and V= 7.65 ft3. • Use the van der Waals EOS.

• Table A-24E. (R= 0.7302 atm.ft3 /(lbmol.oR))

CH4 n-C3H8

a 581 2369 atm.(ft3/lbmol)^2

b 0.685 1.444 ft3/lbmol

Ans. 11.98 RKb

• .a= 1323.9• .b= 1.065• T= 194+459.67 = 653.67 oR• P=49.9 atm

QUIZ #20 OAK

• Find the pressure of a mixture of • CH4 (0.18 kmol) + n-C4H10 (0.274 kmol) • at T=238°C and V= 0.241 m3. • Use the Redlich-Kwong EOS.

• (R=0.08314 bar.m3/kmol.K)

CH4 nC4H10

a 32.11 289.5513

b 0.02965 0.0806

Quiz 21: H-x: Water+H2SO4 Mx

• Find the partial molar enthalpies at 93.3 oC!• water and acid at mass frac. wacid=0.60.

• Also find HTotal at wAcid=0.60 from the relation between PMH and total HT.

H

H H

QUIZ 22: Fugacity of steam PAMRLE

• Calculate the fugacity of steam at • P=60 bar, and T= 500o C • using the steam tables.

h sh s

8.8342