When the gasoline explodes in an automobile cylinder, the temperature is about 2000 K, the pressure is about 8 × 105 Pa, and the volume is about 100 cm3. The piston has cross sectional area 80 cm2. The gas then expands adiabatically (i.e., no heat leaves or enters the cylinder during the process) as the piston is pushed downward, until its volume increases by a factor of 10. For adiabatic expansion of the gas, pVγ = constant, where γ = 1.4.
(a) How much work is done by this gas as it pushes the piston downward?
(b) Assuming it behaves as an ideal gas (pV/T = constant), what is the final temperature of the gas?
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