A perfectly insulated cylinder sits vertically in the back of a delivery truck driving over a bumpy dirt road in the north valley in high summer. Unbeknownst to the driver, inside the cylinder is an explosive stoichiometric mixture of hydrogen and oxygen gases, confined to the cylinder by a weighted piston applying an external pressure of approximately 0.83 atm. The temperature of the gas mixture is initially 90 degrees Fahrenheit, but every time the truck goes over a bump, the temperature rises and falls. While passing over a bump the piston slides in and the pressure reaches 0.90 atm; afterwards the piston moves back out and the pressure drops back to 0.83 atm. The specific heat at constant volume = (5/2)R. (a) If we model a bump as a cycle consisting of two reversible adiabatic processes, a reversible compression increasing the pressure to 0.90 atm, followed by reversible expansion lowering the pressure back to 0.83 atm, what will be the temperature of the gas after 10 complete cycles? (b) If we model each bump-cycle as consisting of two constant-pressure adiabatic processes, a compression taking place at a constant pressure of 0.90 atm, followed by an expansion at constant pressure of 0.83 atm, what will be the temperature of the gas after 10 bumps? A gaseous mixture of hydrogen and oxygen will explode spontaneously if the temperature exceeds 932 degrees Fahrenheit. How many bump-cycles will it take to reach this temperature?
A perfectly insulated cylinder sits vertically in the back of a delivery truck driving over a bumpy dirt road in the north valley in high summer. Unbeknownst to the driver, inside the cylinder is an explosive stoichiometric mixture of hydrogen and oxygen gases, confined to the cylinder by a weighted piston applying an external pressure of approximately 0.83 atm. The temperature of the gas mixture is initially 90 degrees Fahrenheit, but every time the truck goes over a bump, the temperature rises and falls. While passing over a bump the piston slides in and the pressure reaches 0.90 atm; afterwards the piston moves back out and the pressure drops back to 0.83 atm. The specific heat at constant volume = (5/2)R. (a) If we model a bump as a cycle consisting of two reversible adiabatic processes, a reversible compression increasing the pressure to 0.90 atm, followed by reversible expansion lowering the pressure back to 0.83 atm, what will be the temperature of the gas after 10 complete cycles? (b) If we model each bump-cycle as consisting of two constant-pressure adiabatic processes, a compression taking place at a constant pressure of 0.90 atm, followed by an expansion at constant pressure of 0.83 atm, what will be the temperature of the gas after 10 bumps? A gaseous mixture of hydrogen and oxygen will explode spontaneously if the temperature exceeds 932 degrees Fahrenheit. How many bump-cycles will it take to reach this temperature?
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