Randall D. Knight — Heat Engines and Refrigerators: Problem 74

FIGURE CP21.74 shows the Diesel cycle. It is similar to the Otto cycle (see Problem 21.73), but there are two important differences. First, the fuel is not admitted until the air is fully compressed at point 2. Because of the high temperature at the end of an adiabatic compression, the fuel begins to burn spontaneously. (There are no spark plugs in a diesel engine!) Second, combustion takes place more slowly, with fuel continuing to be injected. This makes the ignition stage a constant-pressure process. The cycle shown, for one cylinder of a diesel engine, has a displacement \(V_{max} - V_{min}\) of \(1000 \text{ cm}^3\) and a compression ratio \(r = V_{max}/V_{min} = 21\). These are typical values for a diesel truck. The engine operates with intake air (\(\gamma = 1.40\)) at \(25^{\circ}\text{C}\) and \(1.0 \text{ atm}\) pressure. The quantity of fuel injected into the cylinder has a heat of combustion of \(1000 \text{ J}\). a. Find \(p\), \(V\), and \(T\) at each of the four corners of the cycle. Display your results in a table. b. What is the net work done by the cylinder during one full cycle? c. What is the thermal efficiency of this engine? d. What is the power output in \(\text{kW}\) and horsepower (\(1 \text{ hp} = 746 \text{ W}\)) of an eight-cylinder diesel engine running at \(2400 \text{ rpm}\)?