Question

An air-standard diesel cycle has a compression ratio of 18.2. Air is at 80⁰ F and 14.7 psia at the beginning of the compression process and at 3000 R at the end of the heat addition process. Accounting for the variation of specific heats of air with temperature, determine :

(A) the cutoff ratio,
(B) the heat rejection per unit mass, and
(C) the thermal efficiency.

Answer 1

The air-standard Diesel cycle describes the ideal performance of a Diesel engine. The cutoff ratio, heat rejection per unit mass, and thermal efficiency are found by applying thermodynamic principles and equations to the given temperatures and pressures, considering the specific heat capacities of air.

Step-by-step explanation:

The student's question relates to the air-standard Diesel cycle, which is a model used to simulate the idealized performance of a Diesel engine in thermodynamics.

(A) The cutoff ratio is the ratio of the volume after heat addition (state C) to the volume before heat addition (state B) during the constant pressure process. To find it, we use the fact that the temperature at the end of heat addition is 3000 Rankine (R) and apply the ideal gas law comparison and the relationship between temperature, volume, and pressure during an isobaric (constant pressure) process.

(B) The heat rejection per unit mass involves calculating the amount of heat expelled during the isochoric (constant volume) cooling process from state D to state A. The ideal gas law, combined with the specific heat at constant volume along with the temperatures of the gas before and after the heat rejection process, would be required for this calculation.

(C) The thermal efficiency of the Diesel cycle can be determined using the work output divided by the heat input, or by using the standard thermal efficiency equation for the Diesel cycle, which takes into account both the compression ratio and cutoff ratio, as well as the specific heat ratio of air. The specific heat ratio is typically represented by gamma (γ).