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Q12. A mass of 0.08 kg of helium expands reversibly in a cylinder, according to the law pVⁿ = constant, from a pressure of 8.20 bar and a temperature of 900°C to a pressure of 1.3 bar. The final temperature is 362°C.

(a) Sketch the process on p-V and T-S diagrams.

(b) Determine EACH of the following:

(i) The index of expansion;

(ii) The work transfer;

(iii) The heat transfer;

(iv) The change in entropy.

Note: For Helium, R = 2.077 kJ/kg K and C_p = 5.193 kJ/kg K.

Q15. The thermal efficiency of an air standard Otto cycle is 62% and the indicated mean effective pressure is 850 kN/m². The minimum cycle temperature is 300 K and the minimum cycle pressure is 98 kN/m².

(a) Sketch the cycle on p-V and T-S diagrams.

(b) Determine EACH of the following:

(i) The volume compression ratio;

(ii) The temperature after compression;

(iii) The specific work output;

(iv) The maximum cycle temperature.

Note: For air, C_v = 0.718 kJ/kg K and R = 0.287 kJ/kgK.

Q4. In a 50% reaction turbine stage, steam leaves the fixed blades with a velocity of 220 m/s, the blade/steam speed ratio is 0.70 and the fixed blade outlet angle is 28°. The mean blade ring diameter is 0.81 m.

(a) Sketch the combined velocity diagram, labelling all velocities and angles.

(b) Determine EACH of the following:

(i) The speed of rotation of the turbine rotor;

(ii) The blade inlet angles;

(iii) The diagram efficiency.

Q15. A vapour compression refrigerator uses R134a and operates between pressures of 1.3272 bar and 10.163 bar. The refrigerant enters the compressor at a temperature of -15°C with specific volume 0.15097 m³/kg and the isentropic efficiency of the compressor is 88%. The temperature at outlet from the condenser is 35°C. The cooling load is 50 kW and the volumetric efficiency of the compressor is 0.86.

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

(b) Determine EACH of the following:

(i) The coefficient of performance of the cycle;

(ii) The compressor swept volume rate.

13. A counter flow shell and tube oil cooler has 100 tubes of inside diameter 25 mm and wall thickness 2.5 mm. The tubes are each 2.8 m long. Oil flows in the tubes and water in the shell. The surface heat transfer coefficient on the oil side is 950 W/m² K. The oil enters at a temperature of 82°C and leaves at 45°C and the water enters at 18°C. The mass flow rate of the oil is 8 kg/s and that of the water is 25 kg/s. The specific heat capacities are 2.0 kJ/kg K and 4.2 kJ/kg K for oil and water respectively. Determine EACH of the following:

(a) The rate of heat transfer;

(b) The logarithmic mean temperature difference;

(c) The surface heat transfer coefficient on the water side.

Q13. (a) Sketch the p-V diagram for a two-stage reciprocating air compressor, indicating the area which represents the work saved by intercooling.

(b) In a two-stage reciprocating air compressor, the LP suction pressure is 1.02 bar and the HP delivery pressure is 10.5 bar. The LP suction temperature is 303 K. The index of compression and expansion is 1.3. The HP suction temperature is 310 K, and the HP suction pressure is 3.5 bar.

Determine EACH of the following:

(i) The indicated work per kg of air;

(ii) The heat removed in the intercooler per kg of air;

(iii) The isothermal efficiency.

Note: For air, R = 0.287 kJ/kg K and C_p = 1.005 kJ/kg K.