he pV-diagram in Fig. E20.5 shows a cycle of a heat engine that uses 0.250 mol of an ideal gas with g = 1.40. Process ab is adiabatic. (a) Find the pressure of the gas at point a.  (b) How much heat enters this  gas per cycle, and where does  it happen? (c) How much heat

Consider the following thermodynamic cycle for an ideal gas: From A to B the gas is compressed adiabatically. From B to C heat Qh is added to the gas and the gas is kept at constant volume. From C to D the gas expands adiabatically. From D to A the gas ejects heat Q₁ to the environment and is kept at constant volume. (1) Draw the PV-diagram associated to this cycle. (2) Show that the efficiency of an engine running this cycle is given by e = 1 - (3) Calculate the efficiency for a compression ratio VA/VB = 8 assuming a diatomic gas. [Hint: for a diatomic gas Cv = (5/2)R.]

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A certain gasoline engine is modeled as a monatomic ideal gas undergoing an Otto cycle, represented by the p-V diagram shown in the figure. The initial pressure, volume, and temperature are p1 = 1.05 × 105 Pa, V1 = 0.035 m3, and T1 = 290 K, respectively. a)The first step in the Otto cycle is adiabatic compression. Enter an expression for the work performed on the gas during the first step, in terms of V1, V2, and p1.  b) Calculate the temperature of the gas, in kelvins, at the end of the first step.  c)The fourth and last step in the Otto cycle is isochoric cooling to the initial conditions. Find the amount of heat, in joules, that is discharged by the gas during the fourth step.