Question

Machinist bores a hole of diameter 1.31 cm in a steel plate at a temperature of 25.0 ∘c .

(a) at 25 ℃?
(b) when the temperature of the plate is increased to 175 ℃?
[Coefficient of thermal expansion of steel = 1.2 × 10-5 K-1]​

Answer 1

The change in length of a material due to thermal expansion can be calculated using the equation AL = aLAT. For the steel plate, the change in length at different temperatures can be determined using the given coefficient of thermal expansion. The specific calculations are left as an exercise.

Step-by-step explanation:

The change in length of a material due to thermal expansion can be calculated using the equation AL = aLAT, where AL is the change in length, a is the coefficient of linear expansion, AT is the change in temperature, and L is the initial length of the material. For the steel plate, the coefficient of linear expansion is given as 1.2 × 10-5 K-1.

(a) At 25 °C, the initial length of the plate remains the same, so the change in length is zero.

(b) When the temperature of the plate is increased to 175 °C, the change in temperature is 175 °C - 25 °C = 150 °C. Plugging in this value into the equation, we can calculate the change in length as AL = (1.2 × 10-5 K-1) × (150 °C) × (1.31 cm).

The answer is left as an exercise for you to calculate the final length after the rod is cooled back down to 300 K.