Final answer:
To find the new pressure of a dive tank at a lower temperature, convert temperatures to Kelvin and use Gay-Lussac's Law, which states pressure is directly proportional to absolute temperature when volume is constant. Initial conditions are 3000 psi and 30°C, and final temperature is 14°C.
Step-by-step explanation:
To calculate the change in pressure of a dive tank due to a change in temperature, we can use the Gas Laws, specifically Gay-Lussac's Law for this scenario, as the volume of the tank remains constant and only the temperature and pressure vary. Gay-Lussac's Law states that the pressure of a gas is directly proportional to its absolute temperature when volume is held constant (P/T = constant).
First, convert the temperatures from Celsius to Kelvin (K = °C + 273.15). The initial temperature (T1) is 30°C or 303.15 K, and the final temperature (T2) is 14°C or 287.15 K. Using the formula P2 = P1 * (T2 / T1), where P1 is the initial pressure (3000 psi) and P2 is the final pressure, we calculate the new pressure:
P2 = 3000 psi * (287.15 K / 303.15 K)
Perform the calculation to find P2.