An industrial pneumatic press system utilizes trapped gas to generate force. The gas is in… — Armed Services Vocational Aptitude Battery (ASVAB)

An industrial pneumatic press system utilizes trapped gas to generate force. The gas is initially at an absolute pressure of $30 \text{ psi}$ and occupies a volume of $200 \text{ in}^3$ . During the operation cycle, a mechanical ram pushes down, reducing the gas volume to $50 \text{ in}^3$ while the temperature remains constant. If the face of the piston has a cross-sectional area of $5 \text{ in}^2$ , what is the total upward force, in pounds, exerted by the compressed gas on the piston at this new volume?

Answer: 600 lbs

Answer

600

Since the temperature is constant, Boyle's Law (

P_1V_1 = P_2V_2

) applies. The volume is reduced from

200 \text{ in}^3

50 \text{ in}^3

, which is one-quarter of its original size. Because pressure and volume are inversely proportional for a fixed amount of gas at a constant temperature, the absolute pressure must increase by a factor of four (

30 \text{ psi} \times 4 = 120 \text{ psi}

). The total force exerted by a pressurized fluid on a surface is the product of its pressure and the surface area (

F = P \times A

). Multiplying the new pressure of

120 \text{ psi}

by the piston area of

5 \text{ in}^2

gives a total upward force of

600 \text{ lbs}

Step-by-Step Solution

Calculate the final pressure of the gas after compression.

P_2 = 120 \text{ psi}

According to Boyle's Law, when temperature is constant, the product of absolute pressure and volume is constant (

P_1V_1 = P_2V_2

Calculate the total upward force exerted by the gas.

F = 600 \text{ lbs}

Force is equal to pressure multiplied by the area over which it is applied (

F = P \times A

Key Concept

Combining Boyle's Law for isothermal compression with the basic relationship between pressure, force, and area.

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic