How much will a 300 ft long aluminum pipe grow in length when the temperature rises from 48 degrees to 18 degrees?

How much will a 300 ft long aluminum pipe grow in length when the temperature rises from 48 degrees to 18 degrees?

• A. 7 7/16"
• B. 6 15/16"
• C. 4 13/16"
• D. 3 11/16"

Answer: (A)

To determine how much a 300 ft long aluminum pipe will expand when the temperature rises, it is essential to apply the linear expansion formula: \[ \Delta L = L_0 \times \alpha \times \Delta T \] Where: - \( \Delta L \) is the change in length, - \( L_0 \) is the original length of the pipe (300 ft in this case), - \( \alpha \) is the coefficient of linear expansion for aluminum (approximately \( 0.000012 \, \text{°F}^{-1} \)), - \( \Delta T \) is the change in temperature. First, calculate the change in temperature: \[ \Delta T = 18°F - 48°F = -30°F \] Since the calculation indicates cooling rather than heating, the temperature change becomes: \[ \Delta T = 30°F \] Now applying the values to the formula: \[ \Delta L = 300 \, \text{ft} \times 0.000012 \, \text{°F}^{-1} \times 30°F \] \[ \Delta L = 300 \times 0.000012 \times 30 \] Calculating

To determine how much a 300 ft long aluminum pipe will expand when the temperature rises, it is essential to apply the linear expansion formula:

[ \Delta L = L_0 \times \alpha \times \Delta T ]

Where:

• ( \Delta L ) is the change in length,

• ( L_0 ) is the original length of the pipe (300 ft in this case),

• ( \alpha ) is the coefficient of linear expansion for aluminum (approximately ( 0.000012 , \text{°F}^{-1} )),

• ( \Delta T ) is the change in temperature.

First, calculate the change in temperature:

[ \Delta T = 18°F - 48°F = -30°F ]

Since the calculation indicates cooling rather than heating, the temperature change becomes:

[ \Delta T = 30°F ]

Now applying the values to the formula:

[ \Delta L = 300 , \text{ft} \times 0.000012 , \text{°F}^{-1} \times 30°F ]

[ \Delta L = 300 \times 0.000012 \times 30 ]

Calculating