What is the change in length of a steel rod originally 36" at 68 degrees C when heated to 300 degrees C?

To determine the change in length of the steel rod when it is heated from 68 degrees C to 300 degrees C, it is essential to apply the formula for thermal expansion, which 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 rod (36 inches in this case),

• ( \alpha ) is the coefficient of linear expansion for steel (approximately ( 6.5 \times 10^{-6} , \text{°C}^{-1} )),

• ( \Delta T ) is the change in temperature, calculated as ( 300 - 68 = 232 , \text{°C} ).

Now substituting the values into the formula:

1. Calculate ( \Delta T ):

[

\Delta T = 300 - 68 = 232 , \text{°C}

]

2. Substitute into the thermal expansion formula:

[

\Delta L = 36 , \text{inches} \times 6.5 \