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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 = 0.95 × 105 Pa, V1 = 0.025 m3, and T1 = 310 K, respectively. Part (a)  Calculate the number of moles times the gas constant, nR, in joules per kelvin, to three significant figures, using the ideal-gas law and the initial values of pressure, volume, and temperature. This quantity will be useful for later calculations.  Part (b)  Calculate the work performed on the gas during the first step, in joules, for V2 = V1/6.2.  Part (c)  Calculate the temperature of the gas, in kelvins, at the end of the first step.

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 = 0.95 × 105 Pa, V1 = 0.025 m3, and T1 = 310 K, respectively. Part (a)  Calculate the number of moles times the gas constant, nR, in joules per kelvin, to three significant figures, using the ideal-gas law and the initial values of pressure, volume, and temperature. This quantity will be useful for later calculations.  Part (b)  Calculate the work performed on the gas during the first step, in joules, for V2 = V1/6.2.  Part (c)  Calculate the temperature of the gas, in kelvins, at the end of the first step.

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Problem 6:   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 = 0.95 × 105 Pa, V1 = 0.025 m3, and T1 = 310 K, respectively.

Part (a)  Calculate the number of moles times the gas constant, nR, in joules per kelvin, to three significant figures, using the ideal-gas law and the initial values of pressure, volume, and temperature. This quantity will be useful for later calculations. 

Part (b)  Calculate the work performed on the gas during the first step, in joules, for V2 = V1/6.2. 
Part (c)  Calculate the temperature of the gas, in kelvins, at the end of the first step. 
Part (d)  The second step in the Otto cycle is isochoric (constant-volume) heating. Calculate the heat absorbed by the gas during this process, in joules, if the temperature is increased so that T3 = 1.53T2. 
Part (e)  Calculate the pressure at the end of the isochoric heating step, in pascals, to three significant figures. 
Part (f)  The third step in the Otto cycle is adiabatic expansion, which brings the volume back to its initial value. Calculate the work preformed on the gas, in joules, during the third step. 
Part (g)  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. 
Part (h)  Calculate the efficiency of this Otto cycle, expressed as a percent. 

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Transcribed Image Text:P3, V3, T, V., T, P4, V4, T, P2, V2, T, •P,, V, , T, V
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