Answer :
Final answer:
By applying the combined gas law and converting temperatures to Kelvin and pressures to absolute pressures, we solve for the final volume of compressed gas. The calculation results in approximately 1.461 cubic feet, hence the closest given choice is 1 cubic foot (Option A).
Explanation:
To answer the question about the final volume of a compressed gas, we must use the combined gas law, which relates pressure, volume, and temperature of a gas. The combined gas law is represented by the equation (P1 * V1) / T1 = (P2 * V2) / T2, where P is pressure, V is volume, and T is temperature in Kelvin. To find the final volume (V2), we first need to convert temperatures from Fahrenheit to Kelvin and pressures from psig to absolute pressure (which is psig + 14.7 psi for atmospheric pressure).
First, converting temperatures: 60°F to Kelvin is approximately 288.71 K and 150°F to Kelvin is approximately 338.71 K. We calculate absolute pressures by adding atmospheric pressure: P1 = 70 psig + 14.7 psi ≈ 84.7 psi and P2 = 210 psig + 14.7 psi ≈ 224.7 psi. Now we substitute these values into the combined gas law and solve for V2.
Applying the formula, we get: (84.7 psi * 4 cubic feet) / 288.71 K = (224.7 psi * V2) / 338.71 K. Solving for V2 gives us a final volume of approximately 1.461 cubic feet, which is not exactly one of the options provided, but we can infer that the closest correct choice would be 1 cubic foot (Option A), considering theoretical situations without accounting for real-world gas behaviors and rounding off errors.
