A backup breathing canister has a volume of 50 \text{ in}^3 and stores gas at an absolute … — Armed Services Vocational Aptitude Battery (ASVAB)

A backup breathing canister has a volume of $50 \text{ in}^3$ and stores gas at an absolute pressure of $2000 \text{ psi}$ . During a transfer process, the gas is allowed to expand into a larger holding tank, reaching a total final volume of $250 \text{ in}^3$ . Assuming the temperature remains constant, what is the new absolute pressure of the gas in $\text{psi}$ ?

Answer: 400 psi

Answer

400

According to Boyle's Law, the pressure and volume of a gas are inversely proportional when the temperature is constant (

P_1V_1 = P_2V_2

). Since the volume increased by a factor of 5 (from 50 to 250 cubic inches), the pressure must decrease by a factor of 5. Dividing the initial 2000 psi by 5 gives a final pressure of 400 psi.

Step-by-Step Solution

Identify the initial and final states of the gas.

P_1 = 2000 \text{ psi}

V_1 = 50 \text{ in}^3

, and

V_2 = 250 \text{ in}^3

Organizing the known variables is the first step in solving any gas law problem.

Apply Boyle's Law to relate pressure and volume.

Equation to use:

P_1 V_1 = P_2 V_2

Boyle's Law states that for a fixed mass of gas at constant temperature, pressure and volume are inversely proportional.

Substitute the known values into the equation and solve for the final pressure (

P_2

2000 \times 50 = P_2 \times 250

, which simplifies to

100000 = 250 P_2

. Dividing both sides by 250 gives

P_2 = 400

This mathematical calculation yields the new absolute pressure after the gas has expanded.

Key Concept

Boyle's Law (Inverse relationship between pressure and volume)

Alternative Method

Instead of full algebraic substitution, recognize the proportionality: the volume increases by a factor of 5 (

250 / 50 = 5

). Because pressure and volume are inversely proportional, the pressure must be divided by 5. Thus,

2000 \text{ psi} / 5 = 400 \text{ psi}

Estimated Time:45s

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