A sealed pneumatic cylinder in a robotic assembly arm contains air at an absolute pressure… — Armed Services Vocational Aptitude Battery (ASVAB)

A sealed pneumatic cylinder in a robotic assembly arm contains air at an absolute pressure of $20 \text{ psi}$ . The cylinder has an initial internal volume of $60 \text{ cm}^3$ . During a rapid compression stroke at a constant temperature, the piston reduces the volume to $15 \text{ cm}^3$ . What is the new absolute pressure inside the cylinder?

$80 \text{ psi}$ Cevap
B
$5 \text{ psi}$
C
$15 \text{ psi}$
D
$60 \text{ psi}$

Cevap

The absolute pressure increases to

80 \text{ psi}

because reducing the volume by a factor of 4 causes the pressure to multiply by 4.

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

P_1V_1 = P_2V_2

). The initial pressure-volume product is

20 \times 60 = 1200

. To maintain this constant with a new volume of

15 \text{ cm}^3

, the new pressure must be

1200 \div 15 = 80 \text{ psi}

. Alternatively, recognizing that the volume is reduced by a factor of 4 (

60 \div 15 = 4

) means the pressure must increase by a factor of 4 (

20 \times 4 = 80 \text{ psi}

Adım Adım Çözüm

Identify the initial conditions and the relevant gas law.

Initial pressure (

P_1

) is

20 \text{ psi}

and initial volume (

V_1

) is

60 \text{ cm}^3

. Since temperature is constant, use Boyle's Law:

P_1V_1 = P_2V_2

Boyle's Law defines the inversely proportional relationship between the pressure and volume of a gas when temperature remains unchanged.

Set up the equation with the known values.

20 \text{ psi} \times 60 \text{ cm}^3 = P_2 \times 15 \text{ cm}^3

Substituting the given parameters prepares the equation to isolate the unknown final pressure (

P_2

Solve for the final pressure (

P_2

1200 = P_2 \times 15

, which simplifies to

P_2 = \frac{1200}{15} = 80 \text{ psi}

Isolating

P_2

reveals the new absolute pressure after the compression stroke.

Anahtar Kavram

Boyle's Law (Pressure-Volume Inverse Relationship)

Soru

Cevap

Adım Adım Çözüm

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