Faculté de génieGénie mécanique

Faculty of EngineeringMechanical Engineering

MCG2131 - THERMODYNAMICS II

Final Examination Time: 3 hours22 April 2008 Page 1 of 7Prof. W. Hallett

Closed book. Non-programmable calculators only allowed. Steam tables, a psychrometric chart andsome equations are provided at the end of the paper; other data are given with the questions.

1. (6 marks total) Descriptive questions - give brief answers in words. No calculations are required.You may write your answers in point form if you wish.(a) (2 marks) For an ideal Otto cycle, sketch (i) a P-v diagram; (ii) a T-s diagram. Label the eventsin the cycle on each of these diagrams.(b) (2 marks) A sample of moist air is compressed at constant temperature. How does the relativehumidity change and why?(c) (2 mark) How does an increase in excess air affect the efficiency of a combustion process?Explain why.

2 52. (11 marks total) Ethanol (C H OH) burns in a domestic furnace at a pressure of 101.3 kPaaccording to the following stoichiometric equation:

2 5 2 2 2 2 2 2C H OH + 4.0 (O + 3.76 N ) 6 2.0 CO + 3.0 H O + 1.0 O + 15.04 N

The fuel and air enter the furnace at 25°C and the products leave at 40°C. Determine:

(a) (2 marks) the dew point of the products;(b) (4 marks) the amount of water condensed from the products and the product composition aftercondensation, all in kmol/kmol fuel;(c) (5 marks) the heat transfer from the furnace in MJ/kmol fuel.

Data: Ethanol: molecular mass M = 46 kg/kmol, higher heating value HHV = 31.6 MJ/kg.

Product Enthalpies:

2 22 2 CO OH O N

at 40°C (kJ/kmol) 579 504 441 433

(kJ/kmol) - 43 961 - -

MCG2131 - THERMODYNAMICS IIFinal Examination Time: 3 hours22 April 2008 Page 2 of 7

3. (12 marks total)

A room is heated and ventilated by the system shown in the sketch. Outside air enters at point 1 at

1 1 5 5T = 5°C, N = 40%, and is mixed with air returning from the room at T = 25°C, N = 40%. Thisair is then heated and humidified with cool liquid water. The pressure is 100 kPa throughout. Themass flow rate of outside air is = 5 kg dry air/min, while the recirculated air mass flow rate is

also = 5 kg dry air/min.

(a) (5 marks) Determine the temperature and relative humidity of the air at point 2. (b) (2 marks) Assuming that state 4 and state 5 are the same, show all the processes in the systemon a sketch of a psychrometric chart.

(c) (5 marks) Determine the temperature at point 3 and the heat input required in kW.

A psychrometric chart is provided at the end of this paper.

MCG2131 - THERMODYNAMICS IIFinal Examination Time: 3 hours22 April 2008 Page 3 of 7

4. (16 marks total)

1 1The sketch shows a fan jet aircraft engine. A large flow of air enters the fan at T = 0°C, P = 100

2kPa, and is compressed in the fan to P = 170 kPa. A portion of this air is then split off and is

discharged through a nozzle at the back of the engine (the “bypass” air). The remaining air flow

(the “core” flow) then passes through the rest of the engine, comprising the compressor, the highpressure (HP) turbine which drives the compressor, and the low pressure (LP) turbine which drives

3 4the fan. The pressure P = 4200 kPa, and the temperature T = 1400°C. Assume that the isentropic

C Tefficiencies of the fan, the compressor and both turbines are all 0 = 0 = 0.90.

(a) (2 marks) Sketch a T-s diagram for this cycle.

2(b) (4 marks) If the exit temperature from the fan T = 322.7K, determine the compressor work inkJ/kg.(c) (3 marks) Noting that the high pressure turbine drives only the compressor, determine the

5temperature T at the HP turbine outlet.

5(d) (4 marks) Calculate the pressure P at the outlet of the HP turbine.(e) (3 marks) If the core mass flow = 140 kg/s, determine the bypass flow . The low pressure

T LP Fturbine specific work is w = 480 kJ/kg and the fan specific work is w = -50.2 kJ/kg.

PUse constant specific heat, assuming that for air C = 1.01 kJ/kg K, k = 1.4.

The numbers are representative of a large jet engine such as the Rolls-Royce Trent 1000.

MCG2131 - THERMODYNAMICS IIFinal Examination Time: 3 hours22 April 2008 Page 4 of 7

5. (15 marks total)

The sketch shows a steam power cycle with one open feedwater heater. The follow cycle states aregiven:

1: saturated liquid at 50°C

22: P = 0.3 MPa3: saturated liquid

44: P = 5.0 MPa

55: T = 400°C

PThe isentropic efficiency of both pumps is 0 = 80%, and the isentropic efficiency of both turbines

Tis 0 = 90%.

(a) (2 marks) Sketch a T-s diagram of the cycle.

P LP 2(b) (4 marks) Determine the low pressure pump specific work w in kJ/kg and the enthalpy h atthe low pressure pump exit.

T HP 6(c) (4 marks) Determine the high pressure turbine specific work w in kJ/kg and the enthalpy hat the high pressure turbine exit.(d) (5 marks) Calculate the ratio of the mass flow extracted from the turbine to the mass flow

passing through the low pressure pump.

Properties tables are appended to this paper.

Total marks for this paper: 60

MCG2131 - THERMODYNAMICS IIFinal Examination Time: 3 hours22 April 2008 Page 5 of 7

Steam Tables

Saturated Steam - Temperature Table

f f g f gT (°C) P (kPa) v (m /kg) h (kJ/kg) h (kJ/kg) s (kJ/kgK) s (kJ/kg K)3

0.01 0.6113 0.001 0.01 2501.4 0.0000 9.1562

5 0.8721 0.001 20.98 2510.6 0.0761 9.0257

10 1.2276 0.001 42.01 2519.8 0.1510 8.9008

15 1.7051 0.001001 62.99 2528.9 0.2245 8.7814

20 2.339 0.001002 83.96 2538.1 0.2966 8.6672

25 3.169 0.001003 104.89 2547.2 0.3674 8.5580

30 4.246 0.001004 125.79 2556.3 0.4369 8.4533

35 5.628 0.001006 146.68 2565.3 0.5053 8.3531

40 7.384 0.001008 167.57 2574.3 0.5725 8.2570

45 9.593 0.001010 188.45 2583.2 0.6387 8.1648

50 12.349 0.001012 209.33 2592.1 0.7038 8.0763

Saturated Steam - Pressure Table

f f g f gP (kPa) T (°C) v (m /kg) h (kJ/kg) h (kJ/kg) s (kJ/kgK) s (kJ/kg K)3

5 32.88 0.001005 137.82 2561.5 0.4764 8.3951

10 45.81 0.001010 191.83 2584.7 0.6493 8.1502

20 60.06 0.001017 251.4 2609.7 0.8320 7.9085

30 69.10 0.001022 289.23 2625.3 0.9439 7.7686

50 81.33 0.001030 340.49 2645.9 1.0910 7.5939

75 91.78 0.001037 384.39 2663.0 1.2130 7.4564

100 99.63 0.001043 417.46 2675.5 1.3026 7.3594

200 120.23 0.001061 504.70 2706.7 1.5301 7.1271

300 133.55 0.001073 561.47 2725.3 1.6718 6.9919

400 143.63 0.001084 604.74 2738.6 1.7766 6.8959

500 151.86 0.001093 640.23 2748.7 1.8607 6.8213

MCG2131 - THERMODYNAMICS IIFinal Examination Time: 3 hours22 April 2008 Page 6 of 7

Superheated Water Vapour

P = 5.0 MPa

T (°C) h (kJ/kg) s (kJ/kg K)

Sat 2794.3 5.9734

300 2924.5 6.2084

350 3068.4 6.4493

400 3195.7 6.6459

450 3316.2 6.8186

500 3433.8 6.9759

P = 0.3 MPa

T (°C) h (kJ/kg) s (kJ/kg K)

Sat 2725.3 6.9919

150 2761.0 7.0778

200 2865.6 7.3115

250 2967.6 7.5166

300 3069.3 7.7022

400 3275.0 8.0330

Equations and Other Data

Isentropic relation for a perfect gas with constant specific heat:

Reversible work done on an incompressible liquid in steady flow:

MCG2131 - THERMODYNAMICS IIFinal Examination Time: 3 hours22 April 2008 Page 7 of 7

Psychrometric Chart for a total pressure of 100 kPa