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Q1. The initial pressure, volume and temperature of air in a cylinder are 1.0 bar, 0.2 m³ and 25℃ respectively. It is heated at constant volume to a temperature of 600℃ and then reversibly expanded to the original pressure according to the law pV^1.35 = constant.

(a) Calculate EACH of the following:

(i) the work done; (4)

(ii) the change in internal energy in the expansion process; (4)

(iii) the heat transferred in the expansion process; (2)

(iv) the overall change in entropy. (2)

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

Note: for air C_v = 0.718 kJ/kg K and R = 0.287 kJ/kg K

Q3. In an open gas turbine cycle, 4.5 kg/s of air is induced into a rotary compressor at a pressure and temperature of 1 bar and 18℃ respectively.

It is compressed through a pressure ratio of 5:1 with an isentropic efficiency of 0.85.

The hot gases leave the combustion chamber and enter the turbine at a temperature of 810℃, expanding to the initial pressure with an isentropic efficiency 0.88.

The mass flow rate of fuel may be ignored.

(a) Sketch the cycle on a Temperature-specific entropy diagram. (4)

(b) Calculate EACH of the following:

(i) the net power output of the cycle; (6)

(ii) the work ratio; (2)

(iii) the thermal efficiency. (4)

Note:  for air and the hot gas γ = 1.4 and C_p = 1.006 kJ/kgK

Q4. A fuel has a mass analysis of 80% carbon, 15% hydrogen, 1.5% sulphur and 2% water. The remainder being ash.

The fuel is completely burned in 10% excess air.

Calculate EACH of the following:

(a) the stoichiometric air fuel ratio by mass; (6)

(b) the mass of oxygen required to convert the SO₂ in the combustion products to soluble SO₃; (4)

(c) the volumetric analysis of the dry combustion products after the formation of the SO₃. (6)

Note:  Relative Atomic masses: C=12, H=1, O=16 N=14, S=32.

Air contains 23% oxygen by mass

Q4. In a vapour compression plant 0.452 tonne/hour of refrigerant R134a, leaves the evaporator at a pressure of 2.006 bar and temperature of 0℃. It is then compressed with an isentropic efficiency of 0.825 to a pressure of 8.8672 bar.

The refrigerant leaves the condenser with 5 K of sub-cooling.

(a) Sketch the cycle on EACH of the following:

(i) a Pressure-specific enthalpy diagram indicating the refrigeration effect, compressor work and condenser heat rejection; (2)

(ii) a Temperature-specific entropy diagram, indicating superheat and subcooling. (2)

(b) Determine EACH of the following:

(i) the cooling load; (5)

(ii) the compressor power required; (3)

(iii) the heat rejection in the condenser; (2)

(iv) the coefficient of performance when operating as a heat pump. (2)

Q4. Dry saturated steam at 10 bar enters a steam pipe 50 m in length with an inner diameter of 100 mm and wall thickness of 3 mm.

The pipe insulation limits the condensation of the steam to 6%, when the mass flow rate of steam in the pipe is 7200 kg/hr and the air temperature surrounding the pipe is 20℃.

Calculate EACH of the following:

(a) the thickness of the insulation surrounding the pipe; (8)

(b) the percentage reduction in condensation when the thickness of the insulation is doubled. (8)

Note: inner heat transfer coefficient of the pipe = 545 W/m² K

thermal conductivity of steel = 50 W/mK

thermal conductivity of the insulation = 0.5 W/mK

the outer heat transfer coefficient of the pipe may be ignored

Q2. A two-stage, single acting, water cooled, reciprocating air compressor is designed for minimum work and fitted with an after cooler.

It delivers air at the rate of 17 m³/min at free air conditions of 1.01325 bar 0℃.

The air is compressed from a pressure and temperature of 1 bar 33℃ to a pressure of 30 bar and the air leaves the after cooler at a temperature of 45℃.

The law for all expansion and compression processes is pV^1.3 = constant.

(a) Sketch the cycle on a Pressure–Volume diagram. (2)

(b) Calculate EACH of the following:

(i) the stage power; (4)

(ii) the enthalpy rise of the air in each stage; (4)

(iii) the total heat removed by the cooling water. (6)

Note:  for air R = 0.287 kJ/kg K, C_p =1.005 kJ/kg K