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
Maximum temperature is higher
Heat rejection is lower
Combustion is at constant volume

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Engineering Thermodynamics
According to Avogadro's law, for a given pressure and temperature, each molecule of a gas

Occupies volume proportional to its specific weight
Occupies same volume
Occupies volume inversely proportional to its specific weight
Occupies volume inversely proportional to its molecular weight

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