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Q1. A perfect gas for which R = 0.287 kJ/kg K and g = 1.33 expands reversibly in a cylinder according to the law pV^1.48 = constant and then heated at constant volume. The initial pressure is 88 bar, the initial temperature is 1727°C and the final pressure is 1.5 bar. The final volume is twenty times the initial volume.

(a) Sketch the processes on p-V and T-S diagrams. (4)

(b) Determine EACH of the following:

(i) The temperature after expansion; (2)

(ii) The final temperature; (2)

(ii) The net heat transfers per kg; (5)

(iv) The net change in specific entropy. (3)

Q1. The following bara refer to a 20 cylinder 4-stroke diesel engine under test:

Bore diameter 280 mm

Stroke length 330 mm

Speed of rotation 1000 rev/min

Brake torque 86 kN m

Fuel consumption 1.71 tonne/h

Calorific value of fuel 42 MJ/kg

The fuel supply to each cylinder is cut off in turn, and the brake torque is adjusted each time so that the speed returns to 1000 rev/min. The mean value of the torques thus measured is 81.23 kN m. Determine EACH of the following:

(a) The brake power; (2)

(b) The mechanical efficiency; (5)

(c) The brake specific fuel consumption (kg/kW h); (2)

(d) The average value of indicated mean effective pressure;(4)

(e) The brake thermal efficiency. (3)

Q16. The mass analysis of a fuel is: carbon 78%; hydrogen 16%; sulphur 3.2%; water 2% (remainder ash). Determine EACH of the following:

(a) The theoretical air/fuel ratio by mass; (6)

(b) The volumetric analysis of the dry products (i.e excluding H₂O and soluble SO₂) when the fuel is burned completely in 30% excess air; (6)

(c) The dew point temperature of the combustion products if the total pressure is 1.03 bar. (4)

Note: Atomic mass relationships: H = 1; C = 12; O = 16; N = 14; S = 32

Air contains 21% oxygen by volume and 23.3% oxygen by mass.

Q9. A steam power plant consists of turbine, condenser, feed pump and boiler. Steam enters the turbine at a pressure of 50 bar and a temperature of 400°C, and expands to 0.2 bar, dryness fraction 0.9. The steam is then fully condensed without undercooling. Feed pump work may be disregarded. The boiler has an efficiency of 87%. The fuel used has a calorific value of 38 MJ/kg and contains 85% carbon by mass.

It is proposed that the plant be modified to incorporate “carbon capture”, which involves separating the CO₂ from the exhaust gas and pumping it to a storage facility. It is estimated that separating the CO₂ from the flue gases will require 19% of the turbine power output, and pumping the CO₂ will require 40 kJ per kg of CO₂.

Determine the overall thermal efficiency of the plant:

(a) Before modification; (8)

(b) After modification. (8)

Note: Relative atomic masses: C = 12; O = 16

Q1. (a) Define the term degree of reaction relating to a turbine stage.

(b) In a 50% reaction turbine stage the steam leaves the fixed blades with a velocity of 299 m/s. The axial velocity component is 154 m/s and the blade velocity is 200 m/s.

Determine EACH of the following:

(i) The blade inlet and outlet angles

(ii) The blade work per kg

(iii) The diagram efficiency

Q21. A vapour compression cooling cycle using CO₂ operates between pressures of 18.5089 bar and 68.9182 bar. The refrigerant enters the compressor at a temperature of -18°C and leaves the condenser as saturated liquid. The temperature at compressor outlet is 103°C.

(a) Sketch the cycle on a p-h diagram. (3)

(b) Using Barasheet Q6, determine the coefficient of performance of the cycle. (6)

(c) State TWO disadvantages and THREE advantages of CO₂ as a refrigerant compared with other refrigerants such as halocarbons, hydrocarbons and ammonia. (7)

Q21. Wet steam at a pressure of 7.0 bar flows in a 5-m long pipe of inside diameter 38 mm and wall thickness 5 mm. The pipe is surrounded with a layer of lagging 15 mm thick. The thermal conductivity of the lagging is 0.05 W/m K and the outside surface heat transfer coefficient is 12 W/m² K. The outside air temperature is 30°C. The thermal resistances of steam film and pipe wall may be disregarded. Determine EACH of the following:

(a) The rate of heat loss; (7)

(b) The outside surface temperature of the lagging; (3)

(c) The increase in the rate of heat loss which would result if the thickness of the lagging were reduced to 10mm

Q21. A reciprocating compressor is to be used to compress methane (CH₄) which enters at a temperature of 300 K and a pressure of 0.95 bar. For safety reasons, the temperature of the methane is not to exceed 400 K. The index of compression is 1.3.

Determine EACH of the following:

(a) The specific gas constant R for methane

(b) The maximum pressure which can safely be obtained in a single stage

(c) The volumetric efficiency of the single stage machine if the clearance volume is 4.5% of the swept volume:

(d) The maximum pressure which can safely be obtained using two stages with perfect intercooling

(e) The isothermal efficiency of the two-stage machine.

Note: Atomic mass relationships: H = 1; C = 12

The universal gas constant is 8.314 kJ/k mol K

Q3. (a) Explain the term choked flow with reference to a convergent nozzle. (4)

(b) Air leaks into an evacuated vessel from the surroundings which are at a pressure of 1.00 bar. The passage through which the air leaks may be considered as a convergent nozzle with exit area 0.8 mm², and the flow within the passage may be assumed isentropic. The temperature of the surroundings is 25°C. Determine the mass flow rate when the pressure in the vessel is:

(i) 0.5 bar; (6)

(ii) 0.8 bar. (6)

Note: For air, g = 1.4 and R = 0.287 kJ/kg K

p_c = p_o × [2/(γ + 1)]^γ/γ-1; a = √γRT