A popular wilderness survival tool is a hand held piston where you put dry bits of plant matter into the piston, put the plunger into the top of the piston, and then hit the piston plunger as hard as you can, causing the gas to contract suddenly, which increases the temperature of the gas inside the gas so fast, that it gets hot enough to make the plant matter catch fire. You have a fire piston with a volume of diatomic gas (air) of 0.2 L, a pressure of 102 kPa and a temperature of 293 K. You hit the piston, and the gas inside heats up to 506 K, which is just hot enough to make the plant matter in the bottom of the piston combust. Because you compressed the piston so quickly, this is an Adiabatic process. Required:
Use the fact that this was an adiabatic process, as well as the Ideal Gas Law, to find the final pressure and volume of the gas in the piston right after you compress the piston.