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Q7. A perfect gas expands reversibly in a cylinder according to the law pV^1.13 = constant and is then cooled at constant volume. The initial pressure is 60 bar, the initial temperature is 1500°C and the final pressure is 2.8 bar. The final volume is five times the initial volume.

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

(b) Calculate EACH of the following:

(i) The temperature after expansion

(ii) The final temperature

(iii) The total heat transfer per kg

(iv) The total change in specific entropy.

Note: For the gas, R = 0.189 kJ/kg K and g = 1.23

Q2. The following data refer to a 4 cylinder 4-stroke diesel engine under test:

Bore diameter 83 mm

Stroke length 92.4 mm

Speed of rotation 2800 rev/min

Brake torque 0.11 kNm

Fuel consumption 7.65 kg/h

Calorific value of fuel 35 MJ/kg

Indicated MEP:

Cylinder 1 7.65 bar

Cylinder 2 7.81 bar

Cylinder 3 7.72 bar

Cylinder 4 7.69 bar

Calculate EACH of the following:

(a) The brake power

(b) The mechanical efficiency

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

(d) The brake thermal efficiency

(e) The value to which the brake torque must be reduced to restore the speed to 2800 rev/min if the fuel supply to cylinder 1 is cut off.

Q6. The mass analysis of a fuel is: carbon 80%; hydrogen 14%; sulphur 3%; water 3%.

Determine EACH of the following:

(a) The theoretical air/fuel ratio by mass

(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

(c) The dew point temperature of the combustion products if the total pressure is 1.0462 bar.

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.

Q18. A vapour compression cooling cycle using CO₂ operates between pressures of 20.9384 bar and 72.1369 bar. The refrigerant enters the compressor at a temperature of -13°C and leaves the condenser as a saturated liquid. The isentropic efficiency of the compressor is 85%.

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

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

(c) State TWO disadvantages and TWO advantages of CO₂ compared with other refrigerants.

Q8. Wet steam at a pressure of 12.0 bar flows in a 10 m long pipe of inside diameter 30 mm and wall thickness 4 mm. The pipe is surrounded with a layer of lagging 20 mm thick. The thermal conductivity of the lagging is 0.04 W/m K and the outside surface heat transfer coefficient is 15 W/m² K. The outside air temperature is 32°C. The thermal resistances of steam film and pipe wall may be disregarded. Determine EACH of the following:

(a) The rate of heat loss

(b) The outside surface temperature of the lagging

(c) The increase in the rate of heat loss which would result if the thickness of the lagging were reduced to 15 mm.

Q7. A reciprocating compressor is to be used to compress CO₂ which enters at a temperature of 20°C and a pressure of 15.0 bar. The delivery temperature is not to exceed 100°C. The index of compression is 1.2. Calculate EACH of the following:

(a) The specific gas constant R for CO₂

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

(c) The volumetric efficiency of the single stage machine if the clearance volume is 5% of the swept volume

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

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

Note: Atomic mass relationships: O = 16; C = 12

The universal gas constant is 8.314 kJ/kmol K