Reference no: EM132379904

Part 1:

Question 1. Determination the properties v, u, h and s of H₂O when:
(a) P = 5 bar and t = 29 ºC.
(b) P = 5 bar and x = 0.6.
(c) P = 5 bar and t = 300 ºC.

Question 2. A certain amount of air (R = 0.287 kJ/kg K, C_v = 0.718 kJ/kg K) at a pressure of 5 bar and a temperature of 150 ºC is kept in a container of a fixed volume of 1000 cm³. Determine the following items for the air:
(a) Mass.
(b) Molecular mass.
(c) C_P and γ.
(d) u and h.

Question 3. Air at 1 bar and 25 ºC (R = 0.287 kJ/kg K, C_V = 0.718 kJ/kg K) is compressed to 6 bar adiabatically and reversibly in the cylinder of a reciprocating air compressor. Determine the final temperature, the heat and the work required to perform the compression per unit mass of air.

Question 4. (a) A mass of 0.05 kg of steam containing in a rigid vessel at the pressure of 15 bar has a fixed volume of 0.0076 m³. Determine the steam temperature.

(b) If the vessel is cooled, at what temperature will the steam become just saturated?

(c) If cooling is continued until the pressure in the vessel is 11 bar, determine the final dryness fraction of the steam.

(d) Determine the amount of heat transfer between the initial and the final states.

(e) Sketch the entire cooling process on a t - v diagram.

Question 5. Combustion gases (C_P = 1.2 kJ/kg K and C_V = 0.9 kJ/kg K) at 5 bar and 500 ºC expand through a gas turbine to 1 bar through an isentropic process with a mass flow rate of 0.1 kg/s. Determine the final temperature of the combustion gases by assuming them to be a perfect gas. Determine also the heat transfer and the power output of the turbine.

Question 6. Steam at 2 MPa and 280 ºC enters a nozzle with 20 m/s. During the expansion process, its specific enthalpy drops to 2.89 MJ/kg. Determine the exit velocity from the nozzle.

Question 7.(a) Determine relative humidity, humidity ratio, specific enthalpy and density of atmospheric air at 30°C DB and 23°C WB.

(b) Determine the resultant specific enthalpy when 1.2 kg/s of air at 30°C DB and 23°C WB is mixed adiabatically with 1.5 kg/s of air at 22°C DB and 60% RH.

Question 8. A mass flow rate of 1.5 kg/s of air at 22°C DB and 60% RH is heated to 30°C DB and 50% RH. Determine the rates of heat supply and water vapor added/reduced. Describe the air-conditioning components required to carry out the processes.

Question 9. A mass flow rate of 1.5 kg/s of air at 30°C DB and 70% RH is cooled to 25°C DB and 70% RH. Determine the rates of heat removal/addition and water vapor added/reduced. Describe the air-conditioning components required to carry out the processes.

Question 10. The "SPD Restaurant" having an internal volume of 750 m³ requires installation of an air-conditioning system. After preliminary assessment of the room, its sensible cooling load is estimated to be 12 kW whereas latent cooling load is 8.5 kW. Due to energy saving and human comfort consideration, re-circulating air should be used once the fresh air requirement is fulfilled, and temperature increased by the air supply should be limited to 8ºC after circulating through the room. An adiabatic mixing chamber, a cooling coil, a re-heater and a fan (with negligible heat gain) are proposed to form the air-conditioning system. The following information is provided to support the design task:

Designed Room Conditions	24°C DB and 65% RH
Outdoor Air Conditions for Design Purpose	29°C DB and 85% RH
Air Interchange per Hour to Satisfy Fresh Air requirement	3
Latent Heat of H2O at low pressure	2550 kJ/kg

Perform the following tasks related to the proposed air-conditioning system:
(a) Determine specific enthalpy and humidity ratio of the air at exit of the adiabatic mixing chamber;
(b) Determine the heat removal rate and the condensation rate at the cooling coil; and
(c) Determine the heat addition rate at the re-heater.

Question 11. Write the chemical equation and then determine the Air/Fuel ratio by mass when methane (CH4) react with atmospheric air at:
(a) Stoichiometric Air/Fuel Ratio.
(b) The Equivalence Ratio of 0.8.
(c) The Equivalent Ratio of 1.1.
Also, determine volumetric analysis of the DRY combustion products in each case.

Question 12. Domestic cookers burn LPG (70% butane (C₄H₁₀) and 30% propane (C₃H₈) by volume) with fuel lean Air/Fuel mixture of equivalence ratio of 0.9. Determine:
(a) The actual volumetric Air/Fuel Ratio; and
(b) Analysis of the WET combustion products by mass.

Question 13. Octane (C₈H₁₈) is burnt adiabatically in a steady flow of air in a combustion chamber under stoichiometric condition. The air and fuel are supplied to the combustion chamber at 79°C. Show that the adiabatic temperature of the combustion products is approximately at 2029°C without the occurrence of dissociation.

Enthalpy of combustion of octane at 298K with water vapor in products: - 42500 kJ/kg. Molar Mass: H₂ = 2 kg/kmol; O₂ = 32 kg/kmol; N₂ = 28 kg/kmol; C = 12 kg/kmol

Question 14. Octane gas (C₈H₁₈) and atmospheric air premixing at stoichiometric Air/Fuel ratio are compressed in the thermally insulated cylinder of a gas-fired engine to 129°C and then ignited to burn. Determine the adiabatic flame temperature with aid of the attached table.

Internal energy of combustion of octane gas at 25°C when H₂O is in vapor phase is given as: - 3,945,000 kJ/kmol.

Values of C_V in kJ/kg.K:

Temperature (K)	C8H18	O2	N2	CO2	H2O
300	1.5831	0.6582	0.7341
350	1.9061	0.6682	0.7441
1300		0.8652	0.9221	1.109	2.0281
1350		0.8702	0.9291	1.117	2.0591
1400		0.8742	0.9351	1.124	2.0901

Question 15. A steam power plant operating with a Rankine cycle has a boiler pressure of 50 bar and a condenser pressure of 0.5 bar. At the steam boiler exit, the steam is superheated to 350 °C, whereas the feed water is just saturated at the condenser exit. Considering a mass flow rate of steam of 5 kg/s, determine the thermal efficiency and specific steam consumption of the cycle.

Question 16. Recalculate Q15 if the steam is expanding in the turbine with an isentropic efficiency of 0.88.

Question 17. In a Rankine Cycle with One-Reheat-Stage, the boiler (with superheater), re-heater and condenser are operating at constant pressures of 60 bar, 6 bar and 0.4 bar, respectively. A mass flow rate of 3.5 kg/s of steam is produced at 60 bar and 400 ºC in the boiler, which is then expanded through the high-pressure turbine to become saturated steam at the middle pressure of 6 bar. The steam is then reheated at the constant pressure of 6 bar to 300 ºC in the re-heater, before it is further expanded through the low-pressure turbine to 0.4 bar with a dryness fraction of 0.98 at the turbine exit. This low-pressure wet steam is condensed in the condenser at the constant pressure of 0.4 bar to become saturated water at its exit, and it is then delivered to the feed pump. Determine for this cycle by assuming negligible feed pump power:
(a) Isentropic efficiency of the high-pressure turbine;
(b) Isentropic efficiency of the low-pressure turbine;
(c) Thermal efficiency and specific steam consumption.

Question 18. A four-stroke gasoline engine is analyzed with the Air Standard Otto Cycle theory. The engine has a compression ratio of 8:1 and the minimum cycle pressure is 1 bar. The minimum and maximum cycle temperatures are 15°C and 1000°C, respectively.

Determine the following items by taking

C_V = 0.718kJ / kgK ,

C_P = 1.005 kJ / kgK ,

R = 0.287 kJ / kgK and γ = 1.4:
(a) The maximum cycle pressure;
(b) The thermal efficiency; and
(c) The mean effective pressure.

Question 19. A four-stroke diesel engine is analyzed with the Air Standard Diesel Cycle theory. The engine has a compression ratio of 16:1 and the minimum cycle pressure and temperature are 1 bar and 15°C, respectively. Assume heat supply into the cycle is 1350 kJ/kg of air. Determine the following items by taking:

C_V = 0.718kJ / kgK , C_P = 1.005 kJ / kgK ,

R = 0.287 kJ / kgK

and γ = 1.4:

(a) The maximum cycle pressure;
(b) The thermal efficiency; and
(c) The mean effective pressure.

Question 20. A vapor compression refrigeration cycle using R134a-refrigerant operates between evaporator pressure and condenser pressure of 200 kPa and 1000 kPa, respectively. The refrigerant is a superheated vapor at 0 ºC at the evaporator exit and a saturated liquid at the condenser exit. Determine the following items for a unit mass flow rate of refrigerant:
(a) Compressor power input;
(b) Refrigeration effect; and
(c) Coefficient of Performance.

Question 21. Recalculate Q20 if the refrigerant is compressed in the compressor with an isentropic efficiency of 0.8. Also, determine temperature of the refrigerant at the compressor exit.

Question 22. Determine the "Overall Thermal Resistance" of the following one-dimensional steady- state thermal system between the two temperatures (T₁) and (T₂) with negligible radiation (where T₁ > T₂):

(a) Four rectangular blocks with thickness of 4.0 m and thermal conductivities of:

k_A = 1.6 W⁄m. K; k_B = 0.6 W⁄m. K; k_C = 0.8 W⁄m. K; k_D = 2.0 W⁄m. K.

(b) Two concentric circular pipes with axial length of 5.0 m. Thermal conductivities and heat transfer coefficients of:

k_A = 2.2 W⁄m. K ; k_B = 0.3 W⁄m. K ; h_1-A = 16 W⁄m². K ; h_B-2 = 9 W⁄m². K
Temperatures: T₁ at Fluid (1) and T₂ at Fluid (2)

Question 23. For Q22(a) and Q22(b), calculate the heat transfer rate if T₁ = 80 °C and T₂ = 30 °C.

For the case (b), determine temperature at the external surface of the concentric circular pipes.

Question 24. A composite wall as shown below consists of four walls A, B, C and D having the same width. Heat is transferred by convection at both outer surfaces with fluids I and II, respectively. Estimate the heat transfer rate from fluid I to fluid II through a unit width of the wall (i.e. 1 m) by assuming one-dimensional steady-state conduction through the composite wall and negligible radiation. Thermal conductivities of the wall materials are: k_A = 0.7 W/mK; k_B = 1.6 W/mK; k_C = 1.1 W/mK; k_D = 0.5 W/mK.

 

 

Question 25. A vertical wall of 30 m height maintaining at 37 °C is in contact with ambient air at 17 °C. Ambient air is driven up the vertical wall with a mean velocity of 4 m/s. Define:
(a) Whether the situation is a buoyancy-aided mixed convection or buoyancy-opposed mixed convection.
(b) Whether the situation should be analyzed by assuming free convection, forced convection or mixed convection, when:
• Ri > 3 Free Convection
• 3 > Ri > 0.3 Mixed Convection
• 0.3 > Ri Forced Convection

All fluid properties should be evaluated at Fluid Film Temperature.

Question 26. Air at 27°C flows through a horizontal circular pipe subjecting to electrical heating at its wall with a mean velocity of 3 m/s and is heated to 77°C at the pipe exit. The pipe has a diameter of 80 mm. Because of the heating provided at the pipe wall, it is maintained uniformly at a temperature of 110°C. Determine by assuming negligible radiation:
(a) The average heat transfer coefficient between the air flow and the pipe wall.
(b) The pipe length required.

In the following equations, fluid properties are determined at the fluid bulk temperature.
» Laminar Flow, Re_d < 2000 Nu_d = Re_d /16
» Turbulent Flow, 2000 < Re_d Nu_d = 0.023 Re_d ^0.8 Pr ^0.4

Question 27. A horizontal circular pipe of 10m length and 0.1m external diameter has an external surface temperature of 34°C is placed in an engine room of 20°C surrounding temperature. With aid of the following equations (where film temperature should be used as reference temperature), determine the convective heat transfer from the pipe to the room air.

Nu_d = 0.47 (Gr_d Pr)^0.25 , for (Gr_d Pr) < 10⁹

Nu_d = 0.1 (Gr_d Pr)^0.33 , for (Gr_d Pr) > 10⁹

Nu_d = hd/k and Gr_d = gβΔTd³/v² (where: v = μ/ρ)

Question 28. A digital thermometer equipped with thermocouple is used to measure the temperature "T" of a hot gas stream flowing in a thermally insulated duct as shown in the following diagram. The duct wall is maintained at 87 °C while the thermocouple reads 100 °C for the hot gas stream. The heat transfer coefficient between the thermocouple and the hot gas stream is estimated to be: h = 40 W/m²K, and Stefan-Boltzmann constant for radiation is given as: σ = 5.67 x 10^-8 W/m²k⁴. Determine the actual value of "T".

Question 29. An electrical heater having a surface area of 1.2 m² and a surface temperature of 300 °C is placed in a room, where the wall temperature is maintained at 20 °C. Determine the radiation heat transfer from the heater to the room's walls by assuming they are black body. Given: Stefan-Boltzmann Constant, σ = 5.67 (10 -8) W/m²K⁴.

Question 30. A cylindrical enclosure is formed by three surfaces as shown in the following diagram:

(1) a circular flat end plate of diameter of 3m, and (2) a circular flat end plate of diameter of 3m; and they are surrounded by (3) a circular tube of internal diameter of 3m and an axial length of 1.5m. Determine ALL Radiation Shape Factors among these three surfaces.

Question 31. There are two parallel square flat plates of the same size of 2m x 2m exchanging radiation as shown in the following diagram and their separation is 1m. The top plate having an emissivity of 0.9 is maintained at 100°C, whereas the bottom plate having an emissivity of 0.7 is kept at 80°C. Given the Stefan-Boltzmann Constant, σ = 5.67 (10^-8) W/m² K⁴. Determine the radiation heat transfer between them by assuming:
(a) They are two grey opaque bodies placing at large distance.
(b) They are two grey opaque parallel plates placing closely together.
(c) They are two black bodies.

Also, discuss the errors in using these assumed models.

Part 2:

Assignments

Question 1. A certain amount of air (R = 0.287 kJ/kg K, C_v = 0.718 kJ/kg K) at 5 bar and 150 ºC is kept in a container of a fixed volume of 1000 cm³. Determine:
(a) Mass of the air.
(b) Molecular mass of air.
(c) C_P of air.
(d) u and h of the air.

Question 2. (a) A mass of 0.05 kg of steam at 15 bar is contained in a rigid vessel having a fixed volume of 0.0076 m³. Determine the steam temperature.
(b) If the vessel is cooled, at what temperature will the steam be just saturated?
(c) If cooling is continued until the pressure in the vessel is 11 bar, determine the final dryness fraction of the steam.
(e) Determine the amount of heat transfer between the initial and the final states.
(e) Sketch the entire cooling process on a t - v diagram.

Question 3. (a) Steam at 7 bar and 250 ºC enters a pipeline and flows along it at constant pressure. If the steam rejects heat steadily to the surroundings, at what temperature will water droplets begin to form in the vapor?
(b) Assume negligible changes in kinetic energy and potential energy, determine the heat rejected per unit mass flow rate of steam.

Question 4. When a perfect gas at P₁ and T₁ undergoes an isentropic expansion process to P₂ and T₂, show that the relationship between temperatures and pressures is given by: T₂ = T₁(P₂/P₁)^(γ-1)/y

Question 5. Steam at 6 MPa and 500 ºC expands through a turbine to 10 kPa with a mass flow rate of 1 kg/s. At the turbine exit, the steam has a dryness fraction of 0.9. Sketch the process on a t - v diagram and hence determine the power output from the turbine.

Question 6. A certain perfect gas is kept in a vessel covering by a cover. If it is heated in a reversible non-flow constant pressure process from 15 ºC to 95 ºC, the heat required is 1136 kJ/kg. If it is heated in a reversible non-flow constant volume process between the same temperatures, the heat required is 808 kJ/kg. Determine, C_P, C_v, γ, R and molecular mass of the gas. Show both processes on a P - v diagram.

Question 7. 0.01 kg of air at 1 bar and 27 ºC (R = 0.287 kJ/kg K, C_v = 0.718 kJ/kg K) is compressed in the cylinder of a compressor to 5 bar. If the reversible non-flow compression process is a polytropic process with n = 1.25, determine the following:
(a) Determine the final volume of air.
(b) Determine the final temperature of air.
(c) Determine the change in internal energy.
(d) Determine the work required to perform the compression.
(e) Find the heat transfer during the compression process.

Question 8. Air at 1 bar and 25 ºC (R = 0.287 kJ/kg K, C_v = 0.718 kJ/kg K) is compressed adiabatically and reversibly in the cylinder of a reciprocating air compressor to 6 bar. Determine the final temperature, the heat and the work required to perform the compression per unit mass of air.

Question 9. Combustion gases (C_P = 1.2 kJ/kg K and C_v = 0.9 kJ/kg K) at 5 bar and 500 ºC expand through a gas turbine to 1 bar through an isentropic process with a mass flow rate of 0.1 kg/s. Determine the final temperature of the combustion gases by assuming them to be a perfect gas. Determine also the heat transfer and the power output of the turbine.

Question 10. Steam at 2 MPa and 280 ºC enters a nozzle with 20 m/s. During the expansion process, its enthalpy drops to 2.89 MJ/kg. Determine the exit velocity from the nozzle.

Question 11. A steady flow of steam at a mass flow rate of 0.8 kg/s, a pressure of 20 bar, a temperature of 350 ºC and a velocity of 20 m/s expands through a horizontal steam turbine. At the turbine exit, the steam is expanded to a pressure of 0.5 bar, a dryness fraction of 0.9 and a velocity of 120 m/s. If the heat loss to surroundings from the turbine during this expansion process is 30 kW, determine the power output of the turbine. State clearly all the assumptions made and sketch the process on a temperature-volume diagram.

Question 12. A hot water supply system as shown in Figure Q12 consisting of a gas-fired boiler burners Liquefied Petroleum Gas (LPG) to produce steam, which is mixed with cold water in the mixer to supply hot water for a hotel. Determine:
(a) Mass flow rate of wet steam supplied to the mixer.
(b) Mass flow rate of LPG supplied to the steam boiler.

Figure Q12 Hot Water Supply System for Question 12

Steam Boiler: It converts feed water at 20 and 3 bar to wet steam at 3 bar and 0.96 dry by burning LPG having calorific value of 45 MJ/kg. It operates with combustion efficiency (ratio between heat supplied from fuel to heat absorbed by steam) of 60%.
Mixer: Wet steam from the steam boiler is mixed with cold water at 20 to produce 20 l/s of hot water at 50 .

Question 13. An engine manufacturer claims that the thermal efficiency of a new internal combustion engine is 60% when it is operating between a maximum temperature of 800 °C and a minimum temperature of 200 °C. Determine whether it is possible to construct such an engine.

Question 14. A refrigerator is driven by a 2-kW electric motor. Determine its coefficient of performance when its heat removal capacity is 5 kW.

Question 15. A Carnot cycle receives 50 kW of heat at 1000 °C and has a thermal efficiency of 50%. Determine the work output and the temperature at which heat is rejected.

Question 16. Steam at 10 bar and 300 °C is delivered through a pipe with perfect thermal insulation. After travelling a certain length in the pipe, frictional effect causes the pressure dropping to 9 bar. Determine the change in specific entropy of the steam and explain why the process is irreversible.

Part 3:

Question 1. Determine relative humidity and humidity ratio of atmospheric air at 26.67 °C DB and 10 °C dew point temperature.

Question 2. An electric resistance heater is used to heat 0.05 m³/s of air from 15.5 C DB to 32.2 C DB at a humidity ratio is 0.001. Determine the capacity of the heater.

Question 3. A water pipe with a surface temperature of 11°C DB passes through a room, which is maintained at 23.8°C DB. At what RH of the room will moisture condense on the pipe surface?

Question 4. A cake shop has a sensible cooling load of 13.2 kW and a latent cooling load of 4.4 kW. The shop is maintained at 25 C DB and 45% RH. Determine the RSHR (Room sensible heat ratio) and hence draw the RSHR line.

Question 5. A volume flow rate of 9.43 m³/s of atmospheric air at 27.8 C DB and 50% RH is supplied to the cooling coil of an air conditioning unit to produce supplied air at 17.8 °C DB and 16.1 ° C WB at the cooling coil exit. Draw the cooling and dehumidifying process on the psychrometric chart and then determine:
i) The sensible, latent and total capacity of the cooling coil;
ii) The rate of condensation at the cooling coil; and
iii) Comment on the feasibility of the cooling and dehumidifying process between these two end points directly.

Question 6. Sketch the plant layout of a practical HVAC system using both air and water as working fluid. Explain the function of the following items:
i) Chiller.
ii) Cooling coil.
iii) Fan and duct.
iv) Mixing chamber for returned air and outdoor air.
v) Re-heater.

Question 7. Returned air at 22°C DB and 50% RH is mixed with equal flow rate of outdoor air at 30°C DB and 26°C WB. The mixed air is cooled by passing over a cooling coil to achieve an absolute humidity of 0.008 kg/kg. Determine:
i) The dry and wet bulb temperatures and humidity ratio of the mixed air.
ii) The rate of condensation and heat transfer from the mixed air.

Question 8. A hair salon has a sensible heating load of 16 kW and a latent heating load of 6.5 kW. The room conditions are to be maintained at a dry-bulb temperature of 25.5 C and a relative humidity of 50 %. Determine by assuming latent heat of H₂O is 2500 kJ/kg, the required dry-bulb temperature and moisture content of the supplied air when the mass flow rate is:
(a) 1 m³/s; (b) 1.25 m³/s; (c) 1.5 m³/s.

Question 9. The "SPD Restaurant" having an internal volume of 750 m³ requires installation of an air-conditioning system. After preliminary assessment of the room, its sensible cooling load is estimated to be 12 kW whereas latent cooling load is 8.5 kW. Due to energy saving and human comfort consideration, re-circulating air should be used once the fresh air requirement is fulfilled, and temperature increased by the supplied conditioned-air should be limited to 8ºC after circulating through the room. An adiabatic mixing chamber, a cooling coil, a re-heater and a fan (with negligible heat gain) are proposed to form the air-conditioning system. The following information is provided to support the design task:

Designed Room Conditions	24 C DB and 65% RH
Outdoor Air Conditions for Design Purpose	29 C DB and 85% RH
Air Interchange per Hour to Satisfy Fresh Air requirement	3.5

Perform the following tasks related to the proposed air-conditioning system:
(a) Determine specific enthalpy and humidity ratio of the air at exit of the adiabatic mixing chamber;
(b) Determine the heat removal rate and the condensation rate at the cooling coil; and
(c) Determine the heat addition rate at the re-heater.

Question 10. Design the air-conditioning system for "SPD Cafe", which has an internal volume of 800 m³. You can use re-circulating air when fresh air requirement is fulfilled. Temperature increased by the supplied air after circulating through the room is limited to 8 ºC. You can apply the following information:

Planned Room Conditions		Cooling Loads of The Room		Outdoor Air Conditions Adopted for Design Purpose		Air Interchange per Hour to Satisfy Fresh Air Requirement (N)
		Sensible	Latent
C DB	RH (%)	kW	kW	C DB	RH (%)
24	65	20.5	15.5	30	80	4

Apply adiabatic mixing chamber, cooling coil, re-heater and fan (with negligible heat gain) to form the air-conditioning system. Determine the following:
a) The mass flow rate of re-circulating air that can be used;
b) The heat removal rate and the condensation rate at the cooling coil; and
c) The heat addition rate at the re-heater.