A car’s internal combustion engine can be modeled as a heat engine operating between a combustion temperature of 1500oC and an air temperature of 20oC with 30% of the Carnot efficiency. The heat of combustion of gasoline is 47kJ/g. What mass of gasoline is burned to accelerate a 1500kg car from rest to a speed of 30 m/s?
Mass of Gasoline is burned to accelerate is 57 g
The engine's whole effort will be directed towards increasing the car's kinetic energy. Increase in kinetic energy can be calculated as follows. This is also the mechanical output work of the engine.
Because the initial speed is zero , we've
According to the definition of efficiency. We've got
W is work output and is efficiency of engine and Qh is heat taken from the hot reservoir.
which implies that the heat needs to be put in a heat engine to get work done.
Let represent the heat of combustion of gasoline . Given , the mass in gram required to extract heat , then
Finally, consider efficiency: we know that real efficiency is 30% of ideal Carnot engine.
Combining all of these formulas,
Remember that we can substitute difference of degrees Celsius for temperature difference, but we must convert to kelvin for absolute temperature. As a result, we will have
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