How much will a 110-foot length of brass pipe increase in length when the temperature of the water increases from 40°F to 140°F?

How much will a 110-foot length of brass pipe increase in length when the temperature of the water increases from 40°F to 140°F?

• A. 0.5 inches
• B. 0.8 inches
• C. 1.32 inches
• D. 2 inches

Answer: (C)

To determine how much a 110-foot length of brass pipe will increase in length due to a temperature change, we can use the formula for thermal expansion: \[ \Delta L = L_0 \times \alpha \times \Delta T \] where: - \( \Delta L \) is the change in length, - \( L_0 \) is the original length of the pipe, - \( \alpha \) is the coefficient of linear expansion for brass (approximately \( 0.000019 \, \text{°F}^{-1} \)), - \( \Delta T \) is the change in temperature. In this case, the original length \( L_0 \) is 110 feet, which is 1,320 inches (since there are 12 inches in a foot). The temperature change \( \Delta T \) is from 40°F to 140°F, resulting in a temperature increase of 100°F. Plugging these values into the formula: \[ \Delta L = 1320 \, \text{inches} \times 0.000019 \, \text{°F}^{-1} \times 100 \, \text{°F}

To determine how much a 110-foot length of brass pipe will increase in length due to a temperature change, we can use the formula for thermal expansion:

[

\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,

• ( \alpha ) is the coefficient of linear expansion for brass (approximately ( 0.000019 , \text{°F}^{-1} )),

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

In this case, the original length ( L_0 ) is 110 feet, which is 1,320 inches (since there are 12 inches in a foot). The temperature change ( \Delta T ) is from 40°F to 140°F, resulting in a temperature increase of 100°F.

Plugging these values into the formula:

[

\Delta L = 1320 , \text{inches} \times 0.000019 , \text{°F}^{-1} \times 100 , \text{°F}