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Difficulty: Very hardPneumatics and Gas Laws

A sealed pneumatic cylinder initially contains air at a pressure of 40 psi40 \text{ psi}. A mechanical linkage forces the cylinder's internal volume to be reduced to exactly half (1/21/2) of its original volume. Simultaneously, an external heat source causes the absolute temperature of the confined air to double. If this newly pressurized air is then directed into a separate pneumatic actuator with a piston surface area of 5 in25 \text{ in}^2, what is the total theoretical force exerted by this actuator?

  1. A
    32 lbs32 \text{ lbs}
  2. B
    200 lbs200 \text{ lbs}
  3. C
    400 lbs400 \text{ lbs}
  4. 800 lbs800 \text{ lbs}Answer

Answer

The correct force is 800 lbs800 \text{ lbs}.
The correct answer accurately combines two gas law principles before applying fluid power mathematics. First, halving the volume of a gas doubles its pressure (Boyle's Law). Second, doubling the absolute temperature doubles that pressure again (Gay-Lussac's Law). This results in a final system pressure of 160 psi160 \text{ psi}. When applied to a 5 in25 \text{ in}^2 piston, the total force is 160 psi×5=800 lbs160 \text{ psi} \times 5 = 800 \text{ lbs}.

Step-by-Step Solution

1
Determine the effect of the volume change on the gas pressure using Boyle's Law (P1×V1=P2×V2P_1 \times V_1 = P_2 \times V_2).
Since the volume is halved (1/21/2), the pressure must double. 40 psi×2=80 psi40 \text{ psi} \times 2 = 80 \text{ psi}.
In a compressible gas, pressure and volume are inversely proportional when temperature is held constant.
2
Determine the effect of the temperature change on the gas pressure using Gay-Lussac's Law.
Since the absolute temperature is doubled, the pressure must double again. 80 psi×2=160 psi80 \text{ psi} \times 2 = 160 \text{ psi}.
In a confined gas, absolute pressure is directly proportional to absolute temperature.
3
Calculate the force exerted by the actuator using the final pressure and the piston area (F=P×AF = P \times A).
160 psi×5 in2=800 lbs160 \text{ psi} \times 5 \text{ in}^2 = 800 \text{ lbs}.
Force is defined as pressure applied over a specific surface area.

Key Concept

The Combined Gas Law allows simultaneous evaluation of pressure, volume, and temperature changes in a pneumatic system, which is then used to calculate mechanical force.
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Topics

Pneumatics and Gas Laws

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