A scuba diving fills a tank with air at a pressure of 200 atm and a temperature of 20°C. Later during a dive, the pressure inside the tank drops to 150 atm, and the volume remains constant. What is the final temperature inside the tank in °C?
Answer (1)
We can use the Gay-Lussac's Law to solve this problem, which states that the pressure of a gas is directly proportional to its temperature when the volume is held constant. The formula is: P₁/T₁ = P₂/T₂ Where: - P₁ = initial pressure (200 atm) - T₁ = initial temperature (20°C + 273.15 = 293.15 K) Remember to convert Celsius to Kelvin. - P₂ = final pressure (150 atm) - T₂ = final temperature (what we need to find) Let's solve for T₂: T₂ = (P₂ * T₁) / P₁ = (150 atm * 293.15 K) / 200 atm ≈ 220 K Now, convert back to Celsius: 220 K - 273.15 = -53.15 °C Therefore, the final temperature inside the tank is approximately -53.15 °C.
