Pneumatics and Gas Laws Alıştırma Soruları — Armed Services Vocational Aptitude Battery (ASVAB)

Soru 1Soru →

A sealed pneumatic cylinder initially contains air at a pressure of $40 \text{ psi}$ . A mechanical linkage forces the cylinder's internal volume to be reduced to exactly half ( $1/2$ ) 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 $5 \text{ in}^2$ , what is the total theoretical force exerted by this actuator?

32 \text{ lbs}

200 \text{ lbs}

400 \text{ lbs}

800 \text{ lbs}

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Cevap: $800 \text{ lbs}$

Cevap

The correct force is

800 \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 \text{ psi}

. When applied to a

5 \text{ in}^2

piston, the total force is

160 \text{ psi} \times 5 = 800 \text{ lbs}

.

Adım Adım Çözüm

1

Determine the effect of the volume change on the gas pressure using Boyle's Law (

P_1 \times V_1 = P_2 \times V_2

).

Since the volume is halved (

1/2

), the pressure must double.

40 \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 \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 \times A

).

160 \text{ psi} \times 5 \text{ in}^2 = 800 \text{ lbs}

.

Force is defined as pressure applied over a specific surface area.

Anahtar Kavram

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.

Soru 2Soru →

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?

Cevabı ve açıklamayı göster

Cevap: 600

Cevap

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

to

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}

.

Adım Adım Çözüm

1

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

).

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

).

Anahtar Kavram

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

Soru 3Soru →

A heavy-duty pneumatic shock absorber relies on a sealed chamber of air to dampen impacts. Before an impact, the air inside the chamber has an absolute pressure of $90 \text{ psi}$ , occupies a volume of $60 \text{ in}^3$ , and is at a temperature of $300 \text{ K}$ . During a severe impact, the piston rapidly compresses the air volume to $20 \text{ in}^3$ , causing the internal temperature to spike to $400 \text{ K}$ . Assuming no air escapes, what is the new absolute pressure inside the shock absorber?

40 \text{ psi}

120 \text{ psi}

270 \text{ psi}

360 \text{ psi}

Cevabı ve açıklamayı göster

Cevap: $360 \text{ psi}$

Cevap

360 \text{ psi}

The correct answer correctly applies the Combined Gas Law. The volume is reduced to one-third of its original size, which alone would triple the pressure to

270 \text{ psi}

. Simultaneously, the absolute temperature increases by a factor of

4/3

, which further scales the pressure to

270 \times \frac{4}{3} = 360 \text{ psi}

.

Adım Adım Çözüm

1

Identify the initial state (

P_1, V_1, T_1

) and final state (

V_2, T_2

) variables from the problem.

P_1 = 90 \text{ psi}

,

V_1 = 60 \text{ in}^3

,

T_1 = 300 \text{ K}

;

V_2 = 20 \text{ in}^3

,

T_2 = 400 \text{ K}

.

Establishing known parameters is required to use the Combined Gas Law.

2

Set up the Combined Gas Law equation:

\frac{P_1 \times V_1}{T_1} = \frac{P_2 \times V_2}{T_2}

.

\frac{90 \times 60}{300} = \frac{P_2 \times 20}{400}

Since both volume and temperature are changing simultaneously, the combined relationship must be used.

3

Rearrange the formula to isolate the final pressure (

P_2

).

P_2 = P_1 \times \left(\frac{V_1}{V_2}\right) \times \left(\frac{T_2}{T_1}\right)

This setup groups the variables into easy-to-calculate ratios.

4

Substitute the values and calculate the final result.

P_2 = 90 \times \left(\frac{60}{20}\right) \times \left(\frac{400}{300}\right) = 90 \times 3 \times \frac{4}{3} = 360 \text{ psi}

.

Mathematical evaluation yields the final absolute pressure inside the shock absorber.

Anahtar Kavram

Combined Gas Law and Compressibility

Soru 4Soru →

Arrange the following events in the correct chronological order for the extension stroke of a basic single-acting pneumatic cylinder:

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Cevap

The correct sequence is: 1) The control valve is opened, 2) Air flows into the cylinder, 3) Pressure builds against the piston, 4) The piston rod extends.

The chronological sequence follows the fundamental transfer of energy in a pneumatic system. It begins with control (valve opening), followed by fluid transmission (air flowing into the cylinder), followed by energy accumulation (pressure building against the piston due to gas compressibility), and ends with mechanical work (piston extension).

Adım Adım Çözüm

1

Identify the initiating control action

The control valve is opened.

A pneumatic system requires a signal or mechanical actuation to release energy from the compressor or tank.

2

Trace the path of the working fluid

Air enters the cylinder chamber.

Air moves from a region of higher pressure (supply) to lower pressure (cylinder) through the open valve.

3

Determine the physical effect inside the actuator

Pressure builds against the piston.

As air fills the confined space of the cylinder, it exerts uniform pressure on the piston face.

4

Identify the resulting mechanical output

The piston extends.

Once the force of the air pressure is greater than the opposing load and friction, the piston moves outward.

Anahtar Kavram

Pneumatic System Operation and Force Generation

Soru 5Soru →

A mechanic pushes down on the handle of a manual air pump, sealing the valve and compressing the trapped air. If the volume of the air chamber is reduced to exactly one-half of its original size while the temperature remains constant, what happens to the air pressure inside the pump?

The pressure doubles.

The pressure is reduced by half.

The pressure remains exactly the same.

The pressure quadruples.

Cevabı ve açıklamayı göster

Cevap: The pressure doubles.

Cevap

The pressure doubles.

According to Boyle's Law, the pressure of a given mass of an ideal gas is inversely proportional to its volume when the temperature remains constant. Because the mechanic forces the same amount of air into half the space, the air molecules strike the walls of the pump chamber twice as often, causing the pressure to double.

Adım Adım Çözüm

1

Identify the relationship between gas volume and pressure at a constant temperature.

The relationship is inversely proportional, described by Boyle's Law (

P_1V_1 = P_2V_2

).

Understanding this core gas law is necessary to determine the outcome of volume changes in a sealed pneumatic system.

2

Apply the given volume change to the inverse relationship.

Since the volume is multiplied by

1/2

, the pressure must be multiplied by the reciprocal, which is

2

.

To keep the product of pressure and volume constant, halving one variable strictly requires doubling the other.

Anahtar Kavram

Boyle's Law and Gas Compressibility

Tahmini Süre:45s

Soru 6Soru →

A backup breathing canister has a volume of $50 \text{ in}^3$ and stores gas at an absolute pressure of $2000 \text{ psi}$ . During a transfer process, the gas is allowed to expand into a larger holding tank, reaching a total final volume of $250 \text{ in}^3$ . Assuming the temperature remains constant, what is the new absolute pressure of the gas in $\text{psi}$ ?

Cevabı ve açıklamayı göster

Cevap: 400

Cevap

400

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

P_1V_1 = P_2V_2

). Since the volume increased by a factor of 5 (from 50 to 250 cubic inches), the pressure must decrease by a factor of 5. Dividing the initial 2000 psi by 5 gives a final pressure of 400 psi.

Adım Adım Çözüm

1

Identify the initial and final states of the gas.

P_1 = 2000 \text{ psi}

,

V_1 = 50 \text{ in}^3

, and

V_2 = 250 \text{ in}^3

.

Organizing the known variables is the first step in solving any gas law problem.

2

Apply Boyle's Law to relate pressure and volume.

Equation to use:

P_1 V_1 = P_2 V_2

.

Boyle's Law states that for a fixed mass of gas at constant temperature, pressure and volume are inversely proportional.

3

Substitute the known values into the equation and solve for the final pressure (

P_2

).

2000 \times 50 = P_2 \times 250

, which simplifies to

100000 = 250 P_2

. Dividing both sides by 250 gives

P_2 = 400

.

This mathematical calculation yields the new absolute pressure after the gas has expanded.

Anahtar Kavram

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

Alternatif Yöntem

Instead of full algebraic substitution, recognize the proportionality: the volume increases by a factor of 5 (

250 / 50 = 5

). Because pressure and volume are inversely proportional, the pressure must be divided by 5. Thus,

2000 \text{ psi} / 5 = 400 \text{ psi}

.

Tahmini Süre:45s

Soru 7Soru →

A perfectly sealed, rigid steel air compressor tank is left outside in direct sunlight on a very hot summer day. As the temperature of the trapped air inside the tank increases, what will happen to the internal air pressure?

The pressure will increase.

The pressure will decrease.

The pressure will stay constant because the tank volume is fixed.

The pressure will drop as the heated air molecules move faster.

Cevabı ve açıklamayı göster

Cevap: The pressure will increase.

Cevap

The pressure will increase.

According to Gay-Lussac's Law, the pressure of a fixed mass of gas is directly proportional to its temperature when the volume remains constant. As the air inside the rigid steel tank absorbs heat from the sun, the air molecules gain kinetic energy. They move faster and collide with the internal walls of the tank more frequently and with greater force, which results in a higher internal pressure.

Adım Adım Çözüm

1

Identify the relationship between temperature and pressure for a trapped gas.

Gay-Lussac's Law states that pressure is directly proportional to absolute temperature when volume is constant.

The tank is described as 'rigid' and 'perfectly sealed', meaning the volume cannot change.

2

Apply the temperature change to the system.

The sunlight heats the tank, increasing the temperature of the air inside.

To determine the final state of the gas.

3

Determine the outcome based on the direct relationship.

Because temperature increases, pressure must also increase.

Higher temperature means higher kinetic energy; molecules strike the rigid walls harder and more frequently.

Anahtar Kavram

Gay-Lussac's Law (Temperature-Pressure Relationship)

Soru 8Soru →

Place the following operational stages of a basic reciprocating air compressor in their proper sequential order, starting with the introduction of fresh air into the system.

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Cevap

The correct operational sequence begins with the intake of ambient air, followed by the sealing of the inlet valve, then the compression of the trapped air, and finally the discharge of the pressurized air into the tank.

A basic reciprocating compressor operates in a continuous four-stage loop: it draws air in (intake), seals the chamber, squeezes the air into a smaller volume to build pressure (compression), and then pushes that pressurized air out to a tank (discharge).

Adım Adım Çözüm

1

Identify the starting point of the pneumatic cycle.

The cycle must begin by drawing ambient air into the empty cylinder.

An air compressor needs a fresh supply of air to perform any mechanical work.

2

Determine the necessary condition for compression.

The inlet valve must close to seal the chamber.

If the chamber is not sealed, upward movement of the piston would simply push the air back out instead of compressing it.

3

Identify the actual compression action.

The piston moves up to decrease the internal volume.

Decreasing the volume of the sealed gas increases its pressure.

4

Identify the final stage of the cycle.

The outlet valve opens to release the compressed air.

The system must transfer the high-pressure air into the storage tank for future use.

Anahtar Kavram

Reciprocating compressor cycle and basic application of Boyle's Law

Soru 9Soru →

An aircraft's emergency pneumatic blow-down bottle contains nitrogen gas at an absolute pressure of $3000 \text{ psi}$ with an internal volume of $200 \text{ in}^3$ . 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 $600 \text{ in}^3$ . Assuming the temperature remains constant during this rapid expansion, what is the new absolute pressure in the system?

1500 \text{ psi}

1000 \text{ psi}

4500 \text{ psi}

9000 \text{ psi}

Cevabı ve açıklamayı göster

Cevap: $1000 \text{ psi}$

Cevap

The new absolute pressure in the system is

1000 \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 \text{ in}^3

to a total final volume of

600 \text{ in}^3

. Because the volume increased by a factor of 3 (

600 / 200 = 3

), the pressure must decrease by a factor of 3. Dividing the initial

3000 \text{ psi}

by 3 results in

1000 \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

P_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 (

P_1

) =

3000 \text{ psi}

, Initial volume (

V_1

) =

200 \text{ in}^3

, and Final volume (

V_2

) =

600 \text{ in}^3

.

These are the critical parameters needed to solve for the unknown final pressure (

P_2

).

3

Substitute the known values into Boyle's Law and solve for the final pressure (

P_2

).

3000 \times 200 = P_2 \times 600 \rightarrow 600000 = P_2 \times 600 \rightarrow P_2 = 1000 \text{ psi}

.

Isolating

P_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)

Soru 10Soru →

During the operation of a pneumatic nailer, its internal firing reservoir holds a compressed air volume of $20 \text{ in}^3$ at an absolute pressure of $120 \text{ psi}$ . When the trigger is pulled, the air expands into the driver chamber at a constant temperature until the absolute pressure drops to $30 \text{ psi}$ . Based on Boyle's Law, what is the new total volume of the expanded air in cubic inches?

Cevabı ve açıklamayı göster

Cevap: 80

Cevap

80

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

P_1 \times V_1 = P_2 \times V_2

). The pressure drops from 120 psi to 30 psi, which is a factor of 4 decrease. Because the relationship is inversely proportional, the volume must increase by a factor of 4. Therefore, the initial volume of 20 cubic inches is multiplied by 4, resulting in a final volume of 80 cubic inches.

Adım Adım Çözüm

1

Identify the initial and final states of the gas.

Initial pressure

P_1 = 120 \text{ psi}

, Initial volume

V_1 = 20 \text{ in}^3

. Final pressure

P_2 = 30 \text{ psi}

.

Establishing the known parameters is required before applying the appropriate gas law.

2

Apply Boyle's Law formula.

P_1 \times V_1 = P_2 \times V_2

Since the temperature is constant, Boyle's Law relates the pressure and volume of the trapped air.

3

Substitute values and solve for the unknown final volume (

V_2

).

120 \times 20 = 30 \times V_2 \rightarrow 2400 = 30 \times V_2 \rightarrow V_2 = 80

Isolating

V_2

provides the final expanded volume of the air.

Anahtar Kavram

Boyle's Law states that the absolute pressure of a confined gas is inversely proportional to its volume, provided the temperature remains constant.

Alternatif Yöntem

Use proportional reasoning: Observe that the final pressure (30 psi) is exactly one-quarter (1/4) of the initial pressure (120 psi). Because pressure and volume are inversely proportional under constant temperature, the final volume must be four times (4x) the initial volume. 4 × 20 = 80.

Tahmini Süre:1m 0s

Soru 11Soru →

A heavy transport vehicle uses a pneumatic (air) suspension system to maintain a constant ride height regardless of cargo weight. Place the following events in the operation of this pneumatic leveling system in the correct chronological order, starting from the moment a heavy load is placed on the vehicle.

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Cevap

The correct sequence is: load compresses springs, valve detects drop, air flows into springs, increased pressure raises vehicle.

The correct sequence follows the logical physical response of a pneumatic system to an external load. First, the load mechanically compresses the air springs. This downward movement triggers the control valve. The open valve then allows high-pressure air to flow from the reservoir into the springs. Finally, the newly added air increases the internal pressure, expanding the springs to lift the load and reset the system.

Adım Adım Çözüm

1

Identify the initial triggering event.

The addition of heavy cargo forces the vehicle down, compressing the pneumatic springs.

Air is a compressible fluid, so adding weight decreases the volume of the air in the springs until the pressure balances the new weight.

2

Determine the system's mechanical response.

The leveling valve detects this drop in height and opens.

Pneumatic systems require a mechanical or electrical trigger to allow high-pressure air to enter the working components.

3

Trace the flow of the compressed gas.

Air moves from the storage reservoir into the springs.

Gas naturally flows from an area of higher pressure (reservoir) to an area of lower pressure (compressed springs).

4

Identify the final mechanical work performed by the gas.

The added air increases the pressure inside the springs, forcing them to expand and lift the vehicle.

As more gas is introduced into the flexible space, pressure increases, generating enough mechanical force to lift the load.

Anahtar Kavram

Operation of pneumatic control systems and the relationship between air pressure, volume, and mechanical force.

Soru 12Soru →

A pneumatic lifting system uses compressed air to operate a main lifting cylinder. Initially, the cylinder contains $2.0 \text{ m}^3$ of air at an absolute pressure of $100 \text{ kPa}$ . To prepare for a heavy lift, the system's compressor forces the piston inward, reducing the trapped air's volume to $0.5 \text{ m}^3$ . Assuming the temperature of the air remains constant during this process, what is the new absolute pressure inside the cylinder?

100 \text{ kPa}

25 \text{ kPa}

400 \text{ kPa}

200 \text{ kPa}

Cevabı ve açıklamayı göster

Cevap: $400 \text{ kPa}$

Cevap

The new absolute pressure is

400 \text{ kPa}

.

According to Boyle's Law, the pressure of a fixed mass of gas is inversely proportional to its volume, provided the temperature remains constant. The equation is

P_1V_1 = P_2V_2

. By substituting the given values (

100 \text{ kPa} \times 2.0 \text{ m}^3 = P_2 \times 0.5 \text{ m}^3

), we find that reducing the volume to one-quarter of its original size forces the pressure to quadruple, resulting in a final pressure of

400 \text{ kPa}

.

Adım Adım Çözüm

1

Identify the relevant gas law for a situation with changing pressure and volume at a constant temperature.

Boyle's Law (

P_1V_1 = P_2V_2

) applies to this scenario.

The problem specifies a trapped gas undergoing volume compression while maintaining a constant temperature.

2

Extract the known initial and final values from the problem statement.

Initial pressure (

P_1

) =

100 \text{ kPa}

. Initial volume (

V_1

) =

2.0 \text{ m}^3

. Final volume (

V_2

) =

0.5 \text{ m}^3

.

Organizing known variables is necessary before attempting to solve for the unknown final pressure (

P_2

).

3

Substitute the known values into Boyle's Law equation and solve for the unknown final pressure.

100 \times 2.0 = P_2 \times 0.5

. This simplifies to

200 = 0.5P_2

, which yields

P_2 = 400 \text{ kPa}

.

Calculating the algebraic solution provides the final absolute pressure required by the question.

Anahtar Kavram

Boyle's Law (Inverse Relationship of Pressure and Volume)

Soru 13Soru →

A heavy-duty vehicle's pneumatic braking system relies on an accumulator tank to store potential energy. Initially, a volume of $150 \text{ in}^3$ of air is compressed at an absolute pressure of $90 \text{ psi}$ inside the accumulator. When the operator engages the brakes, the air expands isothermally (at a constant temperature) into the connected brake chambers, causing the system's absolute pressure to drop to $30 \text{ psi}$ . What is the total volume that the air now occupies, in cubic inches?

Cevabı ve açıklamayı göster

Cevap: 450

Cevap

450

According to Boyle's Law, the pressure and volume of a confined gas are inversely proportional when the temperature is held constant. The initial state is

90 \text{ psi}

and

150 \text{ in}^3

. The final pressure drops to

30 \text{ psi}

, which is one-third of the original pressure. Therefore, to balance the equation and conserve the quantity of gas, the volume must expand to three times its original size.

150 \times 3 = 450 \text{ in}^3

.

Adım Adım Çözüm

1

Identify the known variables from the scenario.

P_1 = 90 \text{ psi}

,

V_1 = 150 \text{ in}^3

,

P_2 = 30 \text{ psi}

.

Establishing the initial and final states of the gas is necessary to select the correct formula.

2

Select the appropriate gas law.

Use Boyle's Law:

P_1V_1 = P_2V_2

.

The problem states the expansion happens isothermally (constant temperature) and involves inversely proportional pressure and volume changes.

3

Substitute the values and solve for

V_2

.

90 \times 150 = 30 \times V_2

, so

V_2 = 13500 / 30 = 450 \text{ in}^3

.

Mathematical calculation is required to find the unknown final volume.

Anahtar Kavram

Boyle's Law (Pressure-Volume relationship at constant temperature)

Alternatif Yöntem

Instead of using the formula

P_1V_1 = P_2V_2

algebraically, you can use proportional reasoning. The pressure drops from

90 \text{ psi}

to

30 \text{ psi}

, which is a reduction by a factor of 3 (

90 / 30 = 3

). Because pressure and volume are inversely proportional at a constant temperature, the volume must increase by that exact same factor. Therefore, simply multiply the initial volume by 3:

150 \times 3 = 450 \text{ in}^3

.

Tahmini Süre:1m 0s

Soru 14Soru →

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}

5 \text{ psi}

15 \text{ psi}

60 \text{ psi}

Cevabı ve açıklamayı göster

Cevap: $80 \text{ psi}$

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

1

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.

2

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

).

3

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 15Soru →

A mechanical pressure relief valve is installed on a pneumatic air receiver tank to prevent over-pressurization. Arrange the following events in the correct chronological sequence, from the moment the tank begins to over-pressurize until the system stabilizes.

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Cevap

The sequence begins with system pressure exceeding the setpoint. This creates a pneumatic force that overcomes the spring tension, unseating the valve. The compressed air then vents, lowering system pressure until the spring reseats the valve.

The correct operational sequence of a pneumatic relief valve relies on the balance between gas pressure and mechanical spring force. Initially, an over-pressure condition occurs in the tank. Because force equals pressure multiplied by area, this high pressure exerts an upward force on the valve plug. When this pneumatic force exceeds the downward force of the calibrated spring, the plug lifts. This physical unseating creates a pathway, allowing the highly compressed gas to rapidly expand and vent to the lower-pressure atmosphere. As the gas escapes, the internal tank pressure drops until the pneumatic force is weaker than the spring tension, allowing the spring to snap the valve closed again.

Adım Adım Çözüm

1

Identify the initial condition that triggers the safety system.

The air pressure inside the tank rises above the safe setpoint limit.

A pneumatic relief sequence must begin with an over-pressure event.

2

Determine the mechanical interaction between the compressed air and the valve.

The pneumatic force overcomes the mechanical spring tension.

For the valve to operate, fluid force (Pressure × Area) must defeat the physical mechanism keeping it closed.

3

Establish the physical movement resulting from the force imbalance.

The valve plug lifts off its seat to expose the exhaust port.

The net upward pneumatic force pushes the valve open.

4

Identify the behavior of the gas once the pathway is open.

Compressed air escapes into the atmosphere, reducing tank pressure.

Gas naturally expands and flows from areas of high pressure to low pressure.

5

Determine the condition that ends the sequence.

The spring pushes the valve closed as the pneumatic pressure decreases.

When tank pressure drops sufficiently, the pneumatic force is no longer strong enough to resist the spring.

Anahtar Kavram

Pneumatic System Control and Pressure Relief Operations

Pneumatics and Gas Laws

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