Engineering Thermodynamics
Otto cycle efficiency is higher than Diesel cycle efficiency for the same compression ratio and heat input because in Otto cycle

Expansion and compression are isentropic
Heat rejection is lower
Combustion is at constant volume
Maximum temperature is higher

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Engineering Thermodynamics
Work-done during adiabatic expansion is given by (where p1 v1, T1 = Pressure, volume and temperature for the initial condition of gas, p2, v2, T2 = Corresponding values for the final condition of gas, R = Gas constant, and γ = Ratio of specific heats)

(p1 v1 - p2, v2)/(γ - 1)
[m R (T1 - T2)] /(γ - 1)
[m R T1/(γ - 1)][1 - (p2, v2 /p1 v1)]
All of these

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