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Zorluk: OrtaPneumatics and Gas Laws

An aircraft's emergency pneumatic blow-down bottle contains nitrogen gas at an absolute pressure of 3000 psi3000 \text{ psi} with an internal volume of 200 in3200 \text{ in}^3. During an emergency landing gear extension, a valve opens and the gas expands into the actuator lines and cylinders, increasing the total volume occupied by the gas to 600 in3600 \text{ in}^3. Assuming the temperature remains constant during this rapid expansion, what is the new absolute pressure in the system?

  1. A
    1500 psi1500 \text{ psi}
  2. 1000 psi1000 \text{ psi}Cevap
  3. C
    4500 psi4500 \text{ psi}
  4. D
    9000 psi9000 \text{ psi}

Cevap

The new absolute pressure in the system is 1000 psi1000 \text{ psi}.
According to Boyle's Law, when the temperature of a gas is held constant, its pressure and volume are inversely proportional. The gas expanded from an initial volume of 200 in3200 \text{ in}^3 to a total final volume of 600 in3600 \text{ in}^3. Because the volume increased by a factor of 3 (600/200=3600 / 200 = 3), the pressure must decrease by a factor of 3. Dividing the initial 3000 psi3000 \text{ psi} by 3 results in 1000 psi1000 \text{ psi}.

Adım Adım Çözüm

1
Identify the appropriate gas law for a scenario with changing pressure and volume at a constant temperature.
Boyle's Law applies, which is expressed as P1×V1=P2×V2P_1 \times V_1 = P_2 \times V_2.
Boyle's Law dictates that the pressure of a fixed mass of gas is inversely proportional to its volume, provided the temperature remains constant.
2
Identify the known initial and final variables from the problem statement.
Initial pressure (P1P_1) = 3000 psi3000 \text{ psi}, Initial volume (V1V_1) = 200 in3200 \text{ in}^3, and Final volume (V2V_2) = 600 in3600 \text{ in}^3.
These are the critical parameters needed to solve for the unknown final pressure (P2P_2).
3
Substitute the known values into Boyle's Law and solve for the final pressure (P2P_2).
3000×200=P2×600→600000=P2×600→P2=1000 psi3000 \times 200 = P_2 \times 600 \rightarrow 600000 = P_2 \times 600 \rightarrow P_2 = 1000 \text{ psi}.
Isolating P2P_2 algebraically provides the exact pressure after the gas has fully expanded into the larger volume.

Anahtar Kavram

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

Pneumatics and Gas Laws

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