QUIZZES RIEPJCPIγPJEJJJY

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1 Che 3021 Thermodynamics I QUIZZES RIEPJCPIγPJEJJJY

2 QUIZ 1. Find Molecular Weights: 1 1 CO 2 2 NaCl 3 Aspirin C 9 H 8 O 4 CO2 = NaCl = C9H8O4 = PIgPJC

3 Quiz 1. Temperature conversion 1 Convert 94 o F, to (a). Rankine, o R (b). Kelvin, K (c).. Celsius, o C (a). Rankine, o R = (b). Kelvin, K = (c).. Celsius, o C = PIgPJC

4 Quiz 1. Carnot Efficiency 1 In a Carnot engine, the high temperature is 975 o C, and low temperature is 20 o C; what is its thermal efficiency, η? η = PIgPJC

5 Quiz 2. PV Expansion work of ideal gas: PV = nrt For an ideal gas of 0.7 gmol in a cylinder initially at v 1 = 5 liters and P 1 = 5 atm. What is its temperature T 1 (K)? Expansion at constant temperature takes place until v 2 = 10 liters. What is the final pressure P 2 (atm)? What work has been done, W (in J)? T1 = P2 = W = PJE 2 Hints: Find the gas constant, R PJE

6 Quiz 2. Ideal gas calculations: PJE 2 Calculate the volume (in liter) of air (assuming ideal gas, i.e. PV=nRT) at T= 70 o F, 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 (m 3 /kmol) of CO2 (ideal gas) at bar and -195 o F.

7 Piston-Cylinder Heat Transfer pas 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 m 2. 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 m 3 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

8 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 o C and P = 1bar, and (b) T = 440 o C and P = 320 bar. (MC) Find the enthalpy (Btu/lb m ) and entropy (Btu/(lb m,or) for steam at (a) T = 800 o F and P = 100 psia, and (b) T = 450 o F and P = 60 psia.

9 QUIZ 3. Read Steam Tables and Mollier Chart Find specific volume (m 3 /kg) and enthalpy (kj/kg) for Steam at T= 520 o C and P= 200 bar. T.A-5 Find the enthalpy, H, from the Mollier chart at T= 700 o F, and P=60 psia. PJJ-3

10 QUIZ 3. Read Steam Tables: PJJ-3 Find specific volume (m3/kg) and enthalpy (kj/kg) for subcooled liquid water at T= 200 o C and P= 25 bar. T.A-5 At T= 50 o C, 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

11 Quiz 4. (1) Ideal gas calculations: Given a classroom of size: 25 x30 x12, find the air mass (in lb m ) at T = 75 o F and P= 14.7 psia. PV = nrt. (Choose the right value of R). Air s average MW is RIN (2) Use steam tables: What is the specific volume (in m 3 /kg) of water at saturated pressure of 7.85 psia.

12 lbm

13 QUIZ 5. Calculate the Heat Capacity, Cp, of nitrogen at T =298 K RIQ (1) Use the text formula for N 2. For N 2 : Cp/R = α + βt + γt 2 + δt 3 + εt 4.α= β= e-3.γ= 2.324e-6.δ= e-9.ε= e-12 (2) Use the API formula for N 2. For N 2 : Cp* in cal/(gmol.k) B= , C= , D= , E= ,, F=

14 QUIZ #1. OAKRKb11.98 Find the pressure (atm) of a mixture of CH 4 (0. 5 lbmol) + n-c 3 H 8 (0.5 lbmol) at T=194 F and V= 7.65 ft 3. Use the van der Waals EOS. Table A-24E. (R= atm.ft 3 /(lbmol. o R)) CH4 n-c 3 H 8 a atm.(ft3/lbmol)^2 b ft3/lbmol

15 Ans RKb.a= b= T= = o R P=49.9 atm

16 QUIZ #2 OAK Find the pressure of a mixture of CH 4 (0.18 kmol) + n-c 4 H 10 (0.274 kmol) at T=238 C and V= m 3. Use the Redlich-Kwong EOS. (R= bar.m3/kmol.k) CH4 nc4h10 a b

17 QUIZ 5. Calculate the Heat Capacity, Cp, of nitrogen at T =298 K RIQ (1) Use the text formula for N 2. For N 2 : Cp/R.α= β= e-3.γ= 2.324e-6.δ= e-9.ε= e-12 (2) Use the API formula for N 2. For N 2 : Cp* in cal/(gmol.k) B= , C= , D= , E=

18 QUIZ 5. Calculate the enthalpy of steam PJM-4 For 1 kg of steam at P = 15 bar, and T = 280 o C, the specific volume v = m3/kg. The internal energy is u= kj/kg. Use the formula (Definition) of enthalpy to calculate H = U + PV What is this H-value (kj)? kj

19 QUIZ 5. Calculate the enthalpy of steam RIQ H = U + PV What is this H-value (kj)? kj

20 QUIZ 6. PJQ-5

21 QUIZ 4. Use generalized compressibility chart for nitrogen PJM-4 For 1 kmol of nitrogen (N2) at P = 35 bar, and T = 280 o C, what is its compressibility, Z? Use Figure A1 or A2 in the appendix. Z = 1.05

22 QUIZ 7. RIXPJT 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.

23 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 m 3 /kg. Use the Redlich Kwong equation of state and an appropriate Maxwell relation. PJT

24 QUIZ 6.

25 Quiz 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

26 Quiz 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

27 Quiz F18 Use graphical differentiation and Clapeyron eq. to find the heat of vaporization of saturated steam at 120 o C Steam Given the vapor pressure curve of steam. T,C VP

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

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

32 QUIZ 10. Find the velocity of sound in air (in ft/s) at - 40 o F (below 0 o F) using the ideal gas equation Pv = RT. Use k = 1.4. RJE PJZ

33 Example: Velocity of Sound in Air

34 RJH 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 =

35 4.2

36 Quiz 11. Turbine Work output Winnick <133> PKG+PKH Steam at 1000 o F and 1000 psia is fed steadily to an adiabatic turbine (Q=0) at a rate of 125 lb/min. If the outlet steam is 450 o F and 100 psia, what is the work output in (Btu/min, and kw). (Negligible PE and KE changes). Note that 1 Btu/min = watts.

37 Q11: Ans Winnick <133> PKG kw Btu/min

38 QUIZ 12: Pump Heat capacity: C= 1 Btu/(lb*Δ o F)

39 QUIZ 12 (continued)

40 QUIZ 13. Carnot Efficiency In a Carnot engine, the high temperature is 975 o C, and low temperature is 20 o C; what is its thermal efficiency, η? If the Qc = kj, what is the net entropy change (in kj/k) due to heat transfers Q H and Qc in the Cycle? Calculate the work produced in this cycle: W net =? η = 76.5 % RJSPIg

41 QUIZ 14. Entropy change for Id.g. An ideal gas is compressed from T 1 =300 K, v 1 = 10 m 3 /kg to T 2 = 400 K, v 2 = 2 m 3 /kg. Find the Δs in (kj/(kg.k). Constant heat capacity is assumed at C v =1.008 kj/(kg.k). RJSPIg

42 QUIZ 15: Hot/Cold Isentropic Processes: (1) T 1 = 230K, P 1 =100 bar, T 2 = 350K, find P 2? (a) Use Isentropy (Cold): P2/P1 = (b) Use Tables (A22) (Hot): Pr2=?, Pr1=? P2= P1*(Pr2/Pr1)=

43 Quiz 15b Using Cold & Hot Processes RJZPKN <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 o R. The hat capacity ratio k= Cp/Cv=1.4. (a) Use the cold equations to find T2 ( o R), and P2 (atm). (b) Use table A-22E (the hot process) to find T2 ( o R), and P2 (atm). (Interpolate if needed!)

44 QUIZ 16: Hot/Cold Isentropic Processes: (1) T 1 = 230K, P 1 =100 bar, T 2 = 350K, find P 2? (a) Use Isentropy (Cold): P2/P1 = (b) Use Tables (A22) (Hot): Pr2=?, Pr1=? P2= P1*(Pr2/Pr1)=

45 QUIZ 17: Otto Cycle (Hot) for unit mass (1 kg of working fluid) flowing through. Heat addition Q H is 1400 kj/kg during combustion. (a) Compression Stroke (1-2): T 1 = 300K, P 1 =1 bar, r=8.5 (b) Find T2(K), u2(kj/kg) from Table A-22. (c) Use 1 st law for Combust (2-3) : m(u3-u2) = Q H +0 find u3 and T3! (interpolate!) Vr1, Vr2,V2 8.5

46 QUIZ 18: Otto Cycle (Cold) for unit mass (1 kg of working fluid) flowing through. Heat addition Q H is 1400 kj/kg during combustion. (a) Compression Stroke (1-2): T 1 = 300K, P 1 =1 bar, r=8.5 (b) Find T2(K) & u2(kj/kg) =Cv*T2 (c) Use 1 st law for Combustion (2-3) : m(u3-u2) = Q H +0 find u3 =Cv*T3 (kj/kg). Use k=1.4! Cv=0.713 (kj/(kg.δkelvin)) 8.5

47 QUIZ #19. OAKRKb11.98 Find the pressure (atm) of a mixture of CH 4 (0. 5 lbmol) + n-c 3 H 8 (0.5 lbmol) at T=194 F and V= 7.65 ft 3. Use the van der Waals EOS. Table A-24E. (R= atm.ft 3 /(lbmol. o R)) CH4 n-c 3 H 8 a atm.(ft3/lbmol)^2 b ft3/lbmol

48 Ans RKb.a= b= T= = o R P=49.9 atm

49 QUIZ #20 OAK Find the pressure of a mixture of CH 4 (0.18 kmol) + n-c 4 H 10 (0.274 kmol) at T=238 C and V= m 3. Use the Redlich-Kwong EOS. (R= bar.m3/kmol.k) CH4 nc4h10 a b

50 Quiz 21: H-x: Water+H 2 SO 4 Mx Find the partial molar enthalpies at 93.3 o C! water and Hacid at mass frac. w acid =0.60. H Also find H Total at w Acid =0.60 from the relation between PMH and total H T. H

51 QUIZ 22: Fugacity of steam PAMRLE Calculate the fugacity of steam at P=60 bar, and T= 500 o C using the steam tables h s h s

Chapter 6. Using Entropy

Chapter 6. Using Entropy Chapter 6 Using Entropy Learning Outcomes Demonstrate understanding of key concepts related to entropy and the second law... including entropy transfer, entropy production, and the increase in entropy