How much will a steam line that is 200 m long increase in length when carrying steam at 400°C from an ambient temperature of 15°C?

To determine the increase in length of a steam line due to thermal expansion, the formula used is:

[

\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 material,

• (\alpha) is the coefficient of linear expansion for the material, and

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

In this case, the length of the steam line is 200 m, the temperature change from ambient to operating conditions is from 15°C to 400°C, resulting in a temperature change ((\Delta T)) of 385°C. This value is reached by subtracting the ambient temperature from the steam temperature:

[

\Delta T = 400°C - 15°C = 385°C.

]

Next, the coefficient of linear expansion for steel (a common material for steam lines) is typically around (12 \times 10^{-6} /°C).

Now, substituting the values into the formula:

[

\Delta L = 200 , \text{m} \times 12