Q6. A volume of 1 m3 of air at a pressure and temperature of 4 bar and 150ºC respectively expands isentropically to 1 bar, after which 120 kJ of heat is added at constant pressure.
The two processes can be replaced with a single polytropic process operating between the same initial and final states.
(a) Sketch the processes on Pressure-Volume and Temperature-specific entropy diagrams.
(b) Calculate EACH of the following:
(i) The original total work done
(ii) The index of expansion for the single polytropic process
(iii) The total change in entropy.
Note: For air Cp= 1.005 kJ/kgK, R = 0.287 kJ/kgK and γ = 1.4
Q1. A six cylinder 4 stroke diesel engines has a bore of 230 mm and stroke of 600 mm.
The brake mean effective pressure is 8 bar at 900 rev/min and the brake specific fuel consumption is 0.139 kg/kWh when burning a fuel with a calorific value of 46 MJ/kg.
The air to fuel ratio by mass is 28:1 at atmospheric conditions of 0.95 bar and 17ºC.
(a) Show that the brake mean effective pressure is directly proportional to engine torque and independent of speed.
(i) The shaft torque
(ii) The brake thermal efficiency
(iii) The volumetric efficiency of the engine.
Note: For air R = 0.287 kJ/kgK
Q7. A vapour compression refrigeration cycle using Ammonia operates between saturation temperatures of -24ºC and +20ºC. The refrigerant enters the compressor as a dry saturated vapour and during compression the specific entropy increases by 2.95 %. After cooling it enters the expansion valve as a saturated liquid. The compressor has a stroke of 200 mm and a bore of 100 mm, with a volumetric efficiency of 85% at 300 rev/min. The mechanical efficiency of the drive is 90%.
(a) Sketch the cycle on p-h and T-s diagrams.
(i) The mass flow of refrigerant
(ii) The cooling load based on the mass flow obtained Q6 b (i)
(iii) The input power
(iv) The coefficient of performance of the plant, including the mechanical efficiency of the drive.
Q6. A steel pipe 100 mm bore and 10 mm wall thickness carries dry saturated steam at 12 bar. It is covered with a 50 mm layer of moulded insulation which in turn, is covered with a 60 mm layer of felt. This combination gives an outer surface temperature of 30ºC. The felt is to be replaced with a new insulation which will maintain the original heat transfer rate but requires an interface temperature of 82.5ºC between the felt and the insulation. Calculate EACH of the following:
(a) The original rate of heat loss per unit length of pipe
(b) The change in the moulded insulation thickness to maintain the required condition.
Note: Inner surface heat transfer coefficient = 550 W/m2K
Thermal conductivity of moulded insulation = 0.07 W/mK
Thermal conductivity of felt = 0.09 W/mK
Q5. In a single acting two-stage reciprocating air compressor with negligible clearance, 30 m3 of air per minute are compressed through an overall pressure ratio of 16:1.
The initial pressure and temperature are 1 bar and 27ºC respectively.
The pressure ratio in each stage is the same.
The polytropic index for each compression process is 1.35.
Inter-cooling is perfect and the mechanical efficiency of the compressor is 0.92.
(a) Sketch the process on a p-V diagram indicating the work saved by inter-cooling.
(i) The power input to the compressor
(ii) The heat transfer in the inter-cooler
(iii) The heat transfer to the jacket cooling during compression.
Note: For air R = 0.287 kJ/kgK; Cv = 0.718 kJ/kg K
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