Questions: According to Boyle's Law, the pressure, P, of a compressed gas is inversely proportional to the volume, V, of the gas. If the pressure of a sample of gas is 20 pounds per square inch (psi) when its volume is 500 cubic inches, what is the pressure when the volume is 400 cubic inches? 25 psi 40 psi 50 psi 16 psi

According to Boyle's Law, the pressure, P, of a compressed gas is inversely proportional to the volume, V, of the gas. If the pressure of a sample of gas is 20 pounds per square inch (psi) when its volume is 500 cubic inches, what is the pressure when the volume is 400 cubic inches?
25 psi
40 psi
50 psi
16 psi

Transcript text: According to Boyle's Law, the pressure, $P$, of a compressed gas is inversely proportional to the volume, $V$, of the gas.If the pressure of a sample of gas is 20 pounds per square inch ( psi ) when its volume is 500 cubic inches, what is the pressure when the volume is 400 cubic inches? 25 psi 40 psi 50 psi 16 psi

Solution

Solution Steps

Step 1: Understand Boyle's Law

Boyle's Law states that the pressure of a gas is inversely proportional to its volume, which can be expressed as $ P \times V = \text{constant} $.

Step 2: Set Up the Equation

Given that the initial pressure $ P_1 $ is 20 psi and the initial volume $ V_1 $ is 500 cubic inches, we can write the equation as: \[ P_1 \times V_1 = P_2 \times V_2 \]

Step 3: Substitute Known Values

Substitute the known values into the equation: \[ 20 \, \text{psi} \times 500 \, \text{cubic inches} = P_2 \times 400 \, \text{cubic inches} \]

Step 4: Solve for the Unknown Pressure

Solve for $ P_2 $ by dividing both sides of the equation by 400 cubic inches: \[ P_2 = \frac{20 \times 500}{400} \]

Step 5: Calculate the Result

Calculate the value of $ P_2 $: \[ P_2 = \frac{10000}{400} = 25 \, \text{psi} \]