The cylinder in an automobile engine has a radius of about 5 cm. The top of the piston begins its compression stroke at about 23 cm from the head end and travels about 18 cm during the stroke. The gas in the cylinder behaves as an ideal gas with five degrees of freedom per molecule. It begins at 310 K and 1 atm pressure when the piston is at the bottom of its stroke (i.e., fully expanded).
(a) How many moles of gas are in the cylinder?
(b) What are the temperature and pressure of the gas at the end of the adiabatic compression stroke?
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(c) How much work is done on the gas by the piston during the compression stroke?
(d) When the gas is completely compressed, the combustion of the gasoline increases the temperature by another 800 K. What is the temperature now?
(e) How much heat energy has been added to the gas?
(f) How much work is done by the gas as it expands adiabatically back to its starting point?
(g) What is the efficiency of this engine?