(II) A four-cylinder gasoline engine has an efficiency of...

(II) A four-cylinder gasoline engine has an efficiency of 0.22 and delivers 180 $\mathrm{J}$ of work per cycle per cylinder. The engine fires at 25 cycles per second. (a) Determine the work done per second. $(b)$ What is the total heat input per second from the gasoline? (c) If the energy content of gasoline is 130 $\mathrm{MJ}$ per gallon, how long does one gallon last?

(II) A four-cylinder gasoline engine has an efficiency of 0.22
and delivers 180 $\mathrm{J}$ of work per cycle per cylinder. The engine
fires at 25 cycles per second. (a) Determine the work done
per second. $(b)$ What is the total heat input per second from
the gasoline? (c) If the energy content of gasoline is 130 $\mathrm{MJ}$
per gallon, how long does one gallon last?

Key Concepts

Unit Conversion and Time Calculation

Unit conversion and time calculation are critical for linking different measurements such as joules, megajoules, and gallons, as well as for determining how long a given amount of fuel can sustain engine operation. These conversions ensure that energy outputs and inputs are consistently measured and compared over time.

Fuel Energy Density

Fuel energy density is the amount of energy stored per unit volume of the fuel, expressed in terms like megajoules per gallon. This parameter allows for the comparison of the theoretical energy content of a fuel with the actual energy used by the engine, facilitating calculations of runtime based on fuel consumption.

Work and Power Calculation

Work refers to the energy produced per cycle of the engine, and when multiplied by the number of cycles per second and the number of cylinders, it yields the power output (work done per second). This concept is fundamental in analyzing engine performance and power delivery.

Thermodynamic Efficiency

Thermodynamic efficiency is the ratio of the work output produced by the engine to the heat energy input from the fuel. It is a measure of how effectively the engine converts energy stored in fuel into mechanical work, with losses due to friction, thermal dissipation, and other inefficiencies.

Heat Input Calculation

Heat input calculation involves determining the total energy absorbed from the fuel per unit time using the relationship between work output and efficiency. By rearranging the efficiency formula, the total heat energy input can be found, which is essential for understanding fuel consumption and energy conversion.

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