A dive tank is designed and built to be safe if the difference between the pressure inside the tank and the pressure outside the tank does not exceed 12 atm. A diver has the tank filled at the dive store at a temperature of 20o C to a pressure of 10 atm. The diver places the tank into his car and parks the car in the sun where the temperature of the gas in the tank increases to 60o C. Is the tank safe at this temperature?
(P1/T1) = (P2/T2)
Substitute and solve for P2, then compare with p1.
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To determine if the tank is safe at a temperature of 60°C, we need to calculate the new pressure inside the tank using the ideal gas law.
The ideal gas law states that 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.
First, let's convert the temperatures from Celsius to Kelvin:
Initial temperature, T1 = 20°C + 273.15 = 293.15 K
Final temperature, T2 = 60°C + 273.15 = 333.15 K
We have the following information:
Initial pressure, P1 = 10 atm
Volume, V = constant (assumed)
Gas constant, R = constant (assumed)
Now, we can use the ideal gas law to find the new pressure:
(P1/T1) = (P2/T2), where P2 is the new pressure.
Rearranging the equation, we get:
P2 = (P1 * T2) / T1
Substituting the values, we have:
P2 = (10 atm * 333.15 K) / 293.15 K
Calculating further, we find:
P2 ≈ 11.364 atm
Therefore, at a temperature of 60°C, the pressure inside the tank is approximately 11.364 atm, which is within the safe limit of 12 atm. Hence, the tank is safe at this temperature.