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Zorluk: ZorPneumatics and Gas Laws

An industrial pneumatic press system utilizes trapped gas to generate force. The gas is initially at an absolute pressure of 30 psi30 \text{ psi} and occupies a volume of 200 in3200 \text{ in}^3. During the operation cycle, a mechanical ram pushes down, reducing the gas volume to 50 in350 \text{ in}^3 while the temperature remains constant. If the face of the piston has a cross-sectional area of 5 in25 \text{ in}^2, what is the total upward force, in pounds, exerted by the compressed gas on the piston at this new volume?

Cevap: 600 lbs

Cevap

600
Since the temperature is constant, Boyle's Law (P1V1=P2V2P_1V_1 = P_2V_2) applies. The volume is reduced from 200 in3200 \text{ in}^3 to 50 in350 \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 psi×4=120 psi30 \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×AF = P \times A). Multiplying the new pressure of 120 psi120 \text{ psi} by the piston area of 5 in25 \text{ in}^2 gives a total upward force of 600 lbs600 \text{ lbs}.

Adım Adım Çözüm

1
Calculate the final pressure of the gas after compression.
P2=120 psiP_2 = 120 \text{ psi}
According to Boyle's Law, when temperature is constant, the product of absolute pressure and volume is constant (P1V1=P2V2P_1V_1 = P_2V_2).
2
Calculate the total upward force exerted by the gas.
F=600 lbsF = 600 \text{ lbs}
Force is equal to pressure multiplied by the area over which it is applied (F=P×AF = P \times A).

Anahtar Kavram

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

Pneumatics and Gas Laws

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