Explain, in your own words and with your work, how you arrived at this result. Be sure to explain using calculus concepts to best support the work of the game design team.

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You now have the bacteria needed to create the fuel. "Computer, what is the next step in this process?" Your computer responds that the bacteria have given off enough gas (collected in a 18 L closed container) to create the fuel, and that the fuel is developed by increasing the temperature of the gas at a rate such that the pressure will initially rise at a rate of 41.5725 kPa/min (kilopascals per minute). You control the initial rate of change of temperature, and must set this value so that the initial rate of change of pressure is 41.5725 kPa/min. Once you have made this initial adjustment, the system will adjust dynamically until the fuel is created. Your computer informs you that this gas follows the Ideal Gas Law (PV nRT), and that the units for these calculations are already accounted for. This means that no conversions are necessary in your calculations. Some initial values (at time t= 0) are provided below: = Pressure (P) = 96 kPa Volume (V) = 18 L nR (a constant) = 8.3145 kPaL/K Temperature (T) = 311 K What value do you provide to your computer for the initial rate of change of temperature in kelvin/minute? You now have the bacteria needed to create the fuel. "Computer, what is the next step in this process?" Your computer responds that the bacteria have given off enough gas (collected in a 18 L closed container) to create the fuel, and that the fuel is developed by increasing the temperature of the gas at a rate such that the pressure will initially rise at a rate of 41.5725 kPa/min (kilopascals per minute). You control the initial rate of change of temperature, and must set this value so that the initial rate of change of pressure is 41.5725 kPa/min. Once you have made this initial adjustment, the system will adjust dynamically until the fuel is created. Your computer informs you that this gas follows the Ideal Gas Law (PV nRT), and that the units for these calculations are already accounted for. This means that no conversions are necessary in your calculations. Some initial values (at time t= 0) are provided below: = Pressure (P) = 96 kPa Volume (V) = 18 L nR (a constant) = 8.3145 kPaL/K Temperature (T) = 311 K What value do you provide to your computer for the initial rate of change of temperature in kelvin/minute?

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1 Understanding the Ideal Gas Law The Ideal Gas Law PV nRT relates the pressure P volume V amount of ... View the full answer