A steel pipe 36.0 m long, installed when the temperature was $15 ^ { \circ } \mathrm { C }$ is used to transport superheated steam at a temperature of $155 ^ { \circ } \mathrm { C }$ Steel's coefficient of linear expansion is $1.2 \times 10 ^ { - 5 } \mathrm {~K} ^ { - 1 }$ . The pipe is allowed to expand freely when the steam is transported. What is the increase in the length of the pipe when it is used with the superheated steam?
A)60 mm
B)57 mm
C)54 mm
D)64 mm
E)67 mm

Question

Quizplus · Accepted Answer

The increase in length $\Delta L$ can be calculated using the formula $\Delta L = L_0 \alpha \Delta T$, where $L_0 = 36.0 \, \text{m}$, $\alpha = 1.2 \times 10^{-5} \, \text{K}^{-1}$, and $\Delta T = 155^\circ \text{C} - 15^\circ \text{C} = 140 \, \text{K}$. Substituting these values gives $\Delta L = 36.0 \times 1.2 \times 10^{-5} \times 140 = 0.06048 \, \text{m} = 60.48 \, \text{mm}$, which rounds to 60 mm.

A Steel Pipe 36 15∘C15 ^ { \circ } \mathrm { C }15∘C

A Steel Pipe 36 $15 ^ { \circ } \mathrm { C }$