A 3"-diameter, 5"-long gas-piston assembly contains air at STP. (STP: Standard Temperature and Pressure conditions, 300K and 1 atm. At these conditions the air density is approximately 1.2kg/m3.) Calculate the necessary piston displacement in order to increase the pressure to 45 atm (typical of a diesel engine) varying linearly with displacement (i.e. the pressure varies linearly with displacement) during an adiabatic compression that will increase the gas' internal energy by 1.2kJ.