Final answer:
To calculate the volume left in a nitrous cylinder when the gauge falls below 745, you can use the ideal gas law equation and subtract the gauge pressure from the atmospheric pressure.
Step-by-step explanation:
To calculate the volume left in a nitrous cylinder when the gauge falls below 745, you would first need to know the initial volume of the cylinder. Let's assume the initial volume is Vi and the final volume is Vf. You also need to know the initial pressure of the gas inside the cylinder, Pi. Using the ideal gas law equation (PV = nRT), where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin, you can set up the following equation:
PiVi = PfVf
You know that the gauge pressure is the difference between the absolute pressure inside the cylinder and the atmospheric pressure. If the gauge falls below 745, that means the absolute pressure inside the cylinder is less than the atmospheric pressure by 745. You can subtract the gauge pressure from the atmospheric pressure to find the absolute pressure inside the cylinder, Pf. Then, you can rearrange the equation to solve for Vf:
Vf = (Pi/Pf) × Vi