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Q1) A gas with molar mass 44 kg/kmol K and mass 0.021 kg is compressed isothermally at 281 K to ¼ of its original volume. It is then further compressed according to PV^1.25 = C to ½ of its secondary volume.

Calculate the specific gas constant. (2)

Find the work done during the isothermal compression. (2)

Determine the heat transferred of the initial compression. (1)

Calculate EACH of the following:

The final temperature; (2)

The polytropic work done; (2)

The change in entropy in each process. (4)

Draw pV and Ts diagrams. (3)

Note R₀ = 8.314 kJ/kmol K and C_v = 630 J/kg K

Q2) A gas turbine plant operates on the ideal air standard Joule cycle. The min pressure and temperature are 1 bar and 335 K.

The max pressure and temperature are 8 bar and 1020 K.

(a) Sketch the processes on p-V and T-s diagrams. (2)

(b) Calculate EACH of the following:

(i) The temperature at all points; (5)

(ii) The heat supplied per kg; (2)

(iii) The network output per kg; (5)

(iv) The thermal efficiency. (2)

Note: For air C_P = 1.005 kJ/kg K and C_V = 0.718 kJ/kg K

Q3) A single acting 3 stage reciprocating compressor is designed for minimum work with perfect intercooling. It delivers 0.11 kg/s of air from initial conditions of 1.06 bar and 15℃ and has a volume compression ratio of 3.5 for EACH stage according to the law pV^1.25 = C.

(a) Draw graph pV diagram showing intercooling. (3)

(b) Calculate EACH of the following:

(i) Each stage delivery pressure; (5)

(ii) The total indicated power; (5)

(iii) The total rate of heat removed in the intercoolers. (3)

Note: For air C_p = 1.005 kJ/kg K ; C_v = 0.718 kJ/kg K

Q4) A Carnot cycle uses saturated water and steam as the working fluid and operates between pressures of 0.045 bar and 44 bar.

An ideal Rankine Cycle using steam operates between the same pressure as the Carnot cycle above. The steam is dry saturated at the beginning of the expansion, and saturated liquid leaves the condenser.

a) Determine the Carnot thermal efficiency of the cycle. (2)

b) Sketch the Rankine cycle on a T-s diagram. (2)

c) Determine the Rankine cycle thermal efficiency. (12)

Q5) A vapour compression cycle using ammonia has compressor suction and discharge of 3.413 bar and 11.67 bar respectively.

The vapour enters the compressor in a dry saturated state and leaves at a temperature of 105℃. The liquid refrigerant has 4 K of subcooling at the entry to the expansion valve.

(a) Sketch Ph and Ts diagrams. (2)

(b) Determine the following:

(i) The dryness factor entering the evaporator; (3)

(ii) The specific work done; (3)

(iii) The coefficient of performance; (2)

(iv) The isentropic efficiency of the compressor. (4)

Q6) A copper wire of diameter 5 mm carries an electric current, and EACH metre length generates 6.5 watts of heat. The surrounding air is at 12℃ and the surface heat transfer coefficient is 13 W/m² K.

(a) Determine the temperature of the wire. (6)

(b) The wire is to be covered with insulation 1.5 mm thick and K = 0.1 W/mK.

The outer heat transfer coefficient may be assumed to remain the same.

Calculate the reduced temperature of the wire. (10)

Q7) A natural gas consists of the following volumetric composition:

Nitrogen (N₂) (1.8%); Methane (CH₄) (88.6%); Ethane (C₂H₆) (3.5%) and Ethene (C₂H₄) (0.9%); Sulphur (S) (5.2%)

Determine the Stoichiometric volume of air, for the complete combustion of 1 m³. (16)

Note: the composition of air by volume is 21% O₂ and 79% N₂

Q8) a) Explain the difference between impulse and reaction turbines. (1)

(b) In a 50% reaction turbine stage, the steam leaves the fixed blades with a velocity of 300 m/s. The axial velocity component is 145 m/s and the blade velocity is 200 m/s.

Determine EACH of the following:

(i) The blade inlet and outlet angles; (7)

(ii) The blade work per kg of steam; (4)

(iii) The diagram efficiency. (4)

Q9) a) A jet of fresh water 50 mm diameter issues under a head of 24.4 m and strikes a fixed flat plate

Find the force exerted on the plate when

(i)  the plate is perpendicular; (4)

(ii) The plate is inclined at 30 degrees to the axis of the jet. (2)

(b) Oil of density 900 kg/m³ flow through a pipe from point A and to a point B.

At point A the diameter is 125 mm and the pressure is 160 kPa and at point B, which is 2 m below, the diameter is 250 mm and pressure is 210 kPa.

Determine EACH of the following:

(i) The velocity of the oil at point A; (8)

(ii) The mass flow rate of the oil. (2)