The power output of an automobile engine is directly proportional to the mass
of air that can be forced into the volume of the engine's cylinders to react
chemically with gasoline. Many cars have a \(turbocharger\), which compresses
the air before it enters the engine, giving a greater mass of air per volume.
This rapid, essentially adiabatic compression also heats the air. To compress
it further, the air then passes through an \(intercooler\) in which the air
exchanges heat with its surroundings at essentially constant pressure. The air
is then drawn into the cylinders. In a typical installation, air is taken into
the turbocharger at atmospheric pressure (1.01 \(\times\) 10\(^5\) Pa), density
\(\rho\) = 1.23 kg/m\(^3\), and temperature 15.0\(^\circ\)C. It is compressed
adiabatically to 1.45 \(\times\) 10\(^5\) Pa. In the intercooler, the air is
cooled to the original temperature of 15.0\(^\circ\)C at a constant pressure of
1.45 \(\times\) 10\(^5\) Pa. (a) Draw a \(pV\)-diagram for this sequence of
processes. (b) If the volume of one of the engine's cylinders is 575 cm\(^3\),
what mass of air exiting from the intercooler will fill the cylinder at 1.45
\(\times\) 10\(^5\) Pa? Compared to the power output of an engine that takes in
air at 1.01 \(\times\) 10\(^5\) Pa at 15.0\(^\circ\)C, what percentage increase in
power is obtained by using the turbocharger and intercooler? (c) If the
intercooler is not used, what mass of air exiting from the turbocharger will
fill the cylinder at 1.45 \(\times\) 10\(^5\) Pa? Compared to the power output of
an engine that takes in air at 1.01 \(\times\) 10\(^5\) Pa at 15.0\(^\circ\)C, what
percentage increase in power is obtained by using the turbocharger alone?