Answer:
Therefore, the final pressure inside the scuba tank after cooling from 500°C to 25.5°C is 47.4 atm.
Step-by-step explanation:
To calculate the final pressure inside the scuba tank, we can use the ideal gas law, which states:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin.
First, we need to convert the initial temperature from Celsius to Kelvin:
T1 = 500°C + 273.15 = 773.15 K
Next, we need to calculate the number of moles of gas in the tank. We can use the equation:
n = PV/RT
where n is the number of moles, P is the pressure, V is the volume, R is the gas constant, and T is the temperature in Kelvin.
Assuming the volume of the tank remains constant, we can use the same volume for both the initial and final states, so we can cancel out V:
n = P1/RT1
where P1 is the initial pressure and T1 is the initial temperature.
n = (130.0 atm)/(0.08206 L·atm/mol·K × 773.15 K) = 2.009 mol
Now, we can use the same equation to calculate the final pressure, using the final temperature of 25.5°C or 298.65 K:
P2 = nRT2/V
where P2 is the final pressure, T2 is the final temperature, and V is the volume.
P2 = (2.009 mol) × (0.08206 L·atm/mol·K) × (298.65 K) / V
To solve for V, we need to assume a value for the volume of the tank. Let's assume a typical scuba tank volume of 11.1 L.
V = 11.1 L
P2 = (2.009 mol) × (0.08206 L·atm/mol·K) × (298.65 K) / 11.1 L
P2 = 47.4 atm
Therefore, the final pressure inside the scuba tank after cooling from 500°C to 25.5°C is 47.4 atm.