Serway & Jewett — Heat Engines, Entropy, and the Second Law of Thermodynamics: Problem 47

The compression ratio of an Otto cycle as shown in Figure 21.12 is \(V_A/V_B = 8.00\). At the beginning A of the compression process, 500 cm\(^3\) of gas is at 100 kPa and 20.0°C. At the beginning of the adiabatic expansion, the temperature is \(T_C = 750^\circ\)C. Model the working fluid as an ideal gas with \(\gamma = 1.40\). (a) Fill in this table to follow the states of the gas: State T (K) P (kPa) V (cm\(^3\)) A 293 100 500 B C 1 023 D (b) Fill in this table to follow the processes: Process Q (J) W (J) \(\Delta E_{\text{int}}\) (J) A \(\rightarrow\) B B \(\rightarrow\) C C \(\rightarrow\) D D \(\rightarrow\) A ABCDA (c) Identify the energy input \(|Q_h|\), (d) the energy exhaust \(|Q_c|\), and (e) the net output work \(W_{\text{eng}}\). (f) Calculate the thermal efficiency. (g) Find the number of crankshaft revolutions per minute required for a one-cylinder engine to have an output power of 1.00 kW = 1.34 hp. Note: The thermodynamic cycle involves four piston strokes.