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Q8. A perfect gas is heated at constant pressure in a cylinder and then expands reversibly according to the law pV^1.32 = C.

The initial pressure and temperature are 10 bar 527°C respectively.

The final pressure is 1.0 bar and the final volume is twenty times the initial volume.

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

(b) Calculate EACH of the following:

(i) The temperature after heating

(ii) The final temperature

(iii) The net heat transfer per kg of gas

(iv) The net change in specific entropy during the constant pressure process.

Note: For the gas γ = 1.67, C_p = 5.179 kJ/kgK; R =2.078 kJ/kgK

Q9. The layout of a gas turbine plant is shown in Fig Q2. The plant operates between pressures of 0.98 bar and 7.01 bar. All the work produced by the HP turbine drives the compressor.

The LP turbine drives the load. Air enters the compressor at 26°C and the combustion gas enters the HP turbine at 985°C.

The isentropic efficiency of the compressor is 0.84 and that of each turbine is 0.86.

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

(b) Calculate EACH of the following:

(i) The temperature at the HP turbine exhaust

(ii) The pressure at the HP turbine exhaust

(iii) The network output per kg of air.

Q8. A fuel of mass analysis 84% Carbon and 16% Hydrogen is completely burned in air. The dry flue gas analysis shows that they contain 84% Nitrogen by volume.

(a) Use molar volumes to formulate the complete combustion equation in kmol/kg of fuel.

(b) Calculate EACH of the following:

(i) The percentage excess air by volume

(ii) The air fuel ratio by mass.

Note: Relative atomic masses H = 1, C = 12, N = 14, O = 16

Air contains 21% oxygen by volume

Q10. A vapour compression refrigeration cycle using CO₂ operates between pressures of 25.0095 bar and 68.9182 bar. It produces 6 tonnes per day of ice at -8°C, from fresh water at 20°C.

The refrigerant enters the compressor as a dry saturated vapour and leaves at a temperature of 78°C, it is then condensed and enters the expansion valve as saturated liquid.

(a) Sketch the cycle on p-h and T-s diagrams.

(b) Using Datasheet Q6, determine EACH of the following:

(i) The swept volume of the compressor if the volumetric efficiency is 88%

(ii) The compressor power

(iii) The coefficient of performance of the plant.

Note: For Ice: specific heat capacity 2.1 kJ/kgK, Latent heat 335 kJ/kg

For water: specific heat capacity 4.2 kJ/kgK

Q10. In a counter flow oil cooler, the oil flows with a velocity of 1.2 m/s through a single pass of 35 tubes. Each tube has a bore diameter of 15 mm and wall thickness of 1.6 mm. The oil enters at a temperature of 80°C and leaves at a temperature of 30°C. The fresh water coolant enters at a rate of 7 kg/s and a temperature of 24°C. The overall heat transfer coefficient is 2000 W/m²K, referenced to the tube outer surface area. Calculate EACH of the following:

(a) The total mass flow rate of oil

(b) The outlet temperature of the water

(c) The logarithmic mean temperature difference

(d) The length of each tube.

Note: For water: specific heat capacity 4.2 kJ/kgK

For oil: specific heat capacity 2.0 kJ/kgK, density 860 kg/m³

Q9. A single stage, single acting reciprocating air compressor is used to charge a large air receiver.

The bore has a diameter of 750 mm and the stroke has length of 900 mm. The clearance volume is 9.5% of the swept volume and the mechanical efficiency is 86%.

The suction pressure and temperature are 1.0 bar and 25°C respectively.

The delivery pressure is 7.5 bar when running at a speed of 200 rev/min.

The polytropic index for the compression and expansion process is 1.25.

(a) Sketch the process on a p-V diagram.

(b) Calculate EACH of the following:

(i) The power input required

(ii) The maximum theoretical pressure that can be achieved from the given suction conditions

(c) Explain why the mass flow rate of air alters as the delivery pressure increases.

Note: For air R = 0.287 kJ/kgK; C_p = 1.005 kJ/kgK