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Ch 18: A Macroscopic Description of Matter
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoKnight Calc 5th EditionCh 18: A Macroscopic Description of MatterProblema 55
Capitolo 18, Problema 55

The interior of a Boeing 737-800 can be modeled as a 32-m-long, 3.7-m-diameter cylinder. The air inside, at cruising altitude, is 20°C at a pressure of 82 kPa. What volume of outside air, at −40°C and a pressure of 23 kPa, must be drawn in, heated, and compressed to fill the plane?

Guida verificata passo dopo passo
1
Step 1: Calculate the volume of the interior of the Boeing 737-800 using the formula for the volume of a cylinder: \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height (or length). The radius can be found by dividing the diameter by 2.
Step 2: Use the Ideal Gas Law \( PV = nRT \) to determine the number of moles of air \( n \) inside the plane at cruising altitude. Rearrange the equation to \( n = \frac{PV}{RT} \), where \( P \) is the pressure, \( V \) is the volume, \( R \) is the universal gas constant (8.314 J/(mol·K)), and \( T \) is the temperature in Kelvin.
Step 3: Convert the temperature inside the plane from Celsius to Kelvin using \( T(K) = T(°C) + 273.15 \). Similarly, convert the outside air temperature from Celsius to Kelvin.
Step 4: Use the Ideal Gas Law again to calculate the volume of outside air needed to provide the same number of moles \( n \) as calculated in Step 2. Rearrange the equation to \( V = \frac{nRT}{P} \), where \( P \) is the pressure of the outside air, \( T \) is the temperature of the outside air, and \( n \) is the number of moles determined earlier.
Step 5: Substitute the values for \( n \), \( R \), \( T \), and \( P \) into the equation from Step 4 to find the volume of outside air required. Ensure all units are consistent (e.g., pressure in Pascals, volume in cubic meters, temperature in Kelvin).

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Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for understanding how gases behave under different conditions, allowing us to calculate the volume of air needed based on changes in temperature and pressure.
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Ideal Gases and the Ideal Gas Law

Volume of a Cylinder

The volume of a cylinder can be calculated using the formula V = πr²h, where r is the radius and h is the height (or length). In this context, it helps determine the volume of the Boeing 737-800's interior, which is crucial for understanding how much air needs to be processed.
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05:21
Volume Thermal Expansion

Thermodynamics

Thermodynamics is the study of energy transfer and the laws governing heat and work. In this scenario, it is important to consider how the outside air will be heated and compressed, as these processes will affect the air's volume and pressure, impacting the calculations needed to fill the plane.
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The First Law of Thermodynamics
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