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Q2. A perfect gas expands reversibly in a cylinder according to the law pV^1.5 = constant and is then heated at constant volume.

The initial pressure and temperature are 90 bar and 1800℃ respectively.

The final pressure is 2 bar and the final volume is twenty times the initial volume.

(a) Sketch the processes on Pressure-Volume and Temperature-specific entropy diagrams. (4)

(b) Calculate EACH of the following:

(i) the temperature after expansion; (2)

(ii) the final temperature; (2)

(iii) the net change in specific entropy. (8)

Note: For the gas R = 0.287 kJ/kg K and γ = 1.33

Q2. A compression ignition engine working on the ideal dual combustion cycle has a volume compression ratio of 14:1.

The pressure and temperature at the beginning of compression are 0.95 bar and 30℃ respectively. The maximum pressure of the cycle is 44 bar and the constant pressure heat transfer takes place for 1/18 of the stroke.

(a) Sketch the cycle on Pressure-Volume and Temperature-specific entropy diagrams. (4)

(b) Calculate EACH of the following per unit mass of air:

(i) the heat supply; (6)

(ii) the heat rejected; (2)

(iii) the net work output; (2)

(iv) the thermal efficiency. (2)

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

Q3. A pure hydrocarbon fuel is completely burned in air.

The dry flue gas analysis shows they contain 15% carbon dioxide and 2.5% oxygen by volume.

(a) Determine the full combustion equation in kmols per kmol of fuel. (8)

(b) Calculate EACH of the following:

(i) the percentage mass analysis of the fuel; (4)

(ii) the gravimetric analysis of the wet exhaust gas. (4)

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

Air contains 21% oxygen by volume.

Q3. The cooling load in a vapour compression refrigeration plant using CO₂ is 50 kW.

At this load, the refrigerant enters the compressor at a pressure of 17.314 bar and temperature of -14℃. It is then compressed isentropically to a pressure of 54.65 bar and temperature of 68℃.

After cooling the refrigerant enters the expansion valve as a saturated liquid.

The density of the CO₂ at the compressor suction is 34.66 kg/m³.

The four cylinder single acting compressor has a bore and stroke of 100 mm with a volumetric efficiency of 85%.

(a) Sketch the cycle on Pressure-specific enthalpy and Temperature-specific entropy diagrams. (4)

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

(i) the mass flow rate of refrigerant; (3)

(ii) the compressor power; (2)

(iii) the coefficient of performance; (2)

(iv) the compressor speed of rotation (5)

Q2. A two-stage, single acting reciprocating compressor has a clearance volume of 4.5% of the swept volume in each stage. It is used to compress methane (CH₄).

The initial pressure and temperature are 0.95 bar and 25℃ respectively and the maximum temperature of the methane must be limited to 150℃.

The polytropic index for each compression and expansion process process is 1.3 and inter-cooling is perfect.

(a) Sketch the process on a Pressure-Volume diagram indicating the work saved by inter- cooling. (2)

(b) Calculate EACH of the following:

(i) the interstage and delivery pressures; (2)

(ii) the volumetric efficiency of each stage; (2)

(iii) the specific work input; (4)

(iv) the isothemal efficiency. (6)

Note:   Relative atomic masses H = 1, C = 12

The universal gas constant = 8.3145 kJ/kmolK