A sample of gas occupies 100 in^3 at a pressure of 20 psi and a constant temperature. According to the ideal gas law, what would the volume of the gas be if the pressure is increased to 40 psi?

• A. 200 in^3
• B. 50 in^3
• C. 100 in^3
• D. 25 in^3

Answer: (B)

Verified step by step guidance

1. Recognize that the problem involves a gas at constant temperature, so we can apply Boyle's Law, which states that for a fixed amount of gas at constant temperature, the pressure and volume are inversely proportional. Mathematically, this is expressed as \(P_1 \times V_1 = P_2 \times V_2\).
2. Identify the known values from the problem: initial pressure \(P_1 = 20\) psi, initial volume \(V_1 = 100\) in\(^3\), and final pressure \(P_2 = 40\) psi. The final volume \(V_2\) is what we need to find.
3. Rearrange Boyle's Law to solve for the unknown volume \(V_2\): \(V_2 = \frac{P_1 \times V_1}{P_2}\).
4. Substitute the known values into the equation: \(V_2 = \frac{20 \text{ psi} \times 100 \text{ in}^3}{40 \text{ psi}}\).
5. Calculate the expression to find the new volume \(V_2\). This will give the volume of the gas when the pressure is increased to 40 psi at constant temperature.