Consider a steel bar of length 1.5 m at 10 °C. It is heated to raise its temperature to 100 °C.

Calculate:
(a) Increase in length
(b) Final length at 100 °C

(Coefficient of linear thermal expansion of steel is 1.2 × 10⁻⁵ K⁻¹)

The increase in length of the steel bar when heated from 10 °C to 100 °C is 1.62 mm. Therefore, the final length of the bar at 100 °C is 1.50162 m.
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Answered by Anonymous | 2025-07-04

To solve this problem, we will use the formula for linear thermal expansion, which describes how the length of a material changes with temperature.
Definition:
The linear thermal expansion equation is given by: Δ L = L 0 ​ ⋅ α ⋅ Δ T Where:

Δ L is the change in length (in meters).
L 0 ​ is the original length of the object (in meters).
α is the coefficient of linear thermal expansion for the material (in K − 1 ).
Δ T is the change in temperature (in Celsius or Kelvin; the unit is the same since on the same scale they have equal increments).

Given:

L 0 ​ = 1.5 m (initial length of the steel bar).
α = 1.2 × 1 0 − 5 K − 1 (coefficient of linear thermal expansion for steel).
Initial temperature = 10°C.
Final temperature = 100°C.
Δ T = 100° C − 10° C = 90° C .

(a) Increase in length:
Using the linear thermal expansion formula: Δ L = 1.5 × 1.2 × 1 0 − 5 × 90 Δ L = 0.00162 m = 1.62 mm So, the increase in length of the steel bar is 1.62 mm .
(b) Final length at 100°C:
The final length L f ​ is calculated as: L f ​ = L 0 ​ + Δ L L f ​ = 1.5 + 0.00162 L f ​ = 1.50162 m Rounding it to a practical measuring precision:
The final length is approximately 1.5 m when rounded to three significant figures. However, it is crucial to note that adding a small change such as 0.00162 m to 1.5 m practically still rounds to 1.5 m considering typical measurement precision in practical applications.

Answered by AvaCharlotteMiller | 2025-07-06