Thermal efficiency diesel cycle engines

An ideal Diesel cycle with a compression ratio of 20 and a cut-off ratio of 2 has a temperature of 105°F and a pressure of ISpsia at the beginning of the compression process. Determine (a) the temperature and pressure of the gas at the end of the compression process, (b) the temperature and pressure of the gas at the end of the combustion process, (c) heat added to the engine in the combustion chamber, (d) heat removed from the engine to the environment, and (e) thermal cycle efficiency. 

An ideal Diesel engine receives air at 103.4 kPa and 27°C. Heat added to the air is 1016.6 kJ/kg, and the compression ratio of the engine is 13. Determine (a) the work added during the compression process, (b) the cut-off ratio, (c) the work done during the expansion process, (d) the heat removed from the air during the cooling process, (e) the MEP (mean effective pressure), and (f) the thermal efficiency of the cycle. 

A Diesel cycle has a compression ratio of 18. Air-intake conditions (prior to compression) are 72°F and 14.7 psia, and the highest temperature in the cycle is limited to 2500° F to avoid damaging the engine block. Calculate (a) thermal efficiency, (b) net work, and (c) mean effective pressure (d) compare engine efficiency with that of a Carnot cycle engine operating between the same temperatures. 

The Diesel cycle is a compression-ignition reciprocating engine consisting of an isentropic compression process, a constant-pressure combustion process, an isentropic expansion process, and a constant-volume cooling process. The thermal efficiency of the Otto cycle depends on its compression ratio and cut-off ratio. The compression ratio is defined as f max/ f min- The cut-off ratio is defined as — Toombustion off/f min ... 

As an example, if the hot temperature is 1273 K (1000 °C) and the cold temperature 373 K (100 °C) then the efficiency is approximately 70%. In practice the operation of a real engine does not follow the Carnot cycle and the efficiency is considerably lower. For a medium sized motor car with an internal combustion engine the fuel efficiency is about 12%, much of the wasted 88% demanding water cooling. There are continuous improvements made in petrol and diesel engine technologies and in the fuels and projections suggest that thermal efficiencies a little over 50% will eventually be achieved. 

Show that for the same compression ratio the thermal efficiency of the air-standard Otto engine is greater than the themial efficiency of the air-standard Diesel cycle. Hint Show that the fraction which multiplies (l/r) in the above equation for is greater than unity by expanding rc in a Taylor series with the remainder taken to the first derivative. 

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