Question

The coefficient of linear expansion of lead is 29 x 10 K What change in temperature will cause a 5-m long lead bar to change in length by 3.0 mm?

Answer 1

Answer:

These linear thermal expansion coefficients are room temperature values of metals. Linear thermal expansion coefficient is defined as material's fractional change in length divided by the change in temperature.

Explanation:

Answer 2

The change in temperature caused is 0.0000207 K.

To calculate the change in temperature we use the formula of linear expansivity below.

⇒ Formula:

• ∝ = ΔL/(LΔT).................. Equation 1

⇒ Where:

• ∝ = Coefficient of linear expansion
• ΔL = Change in length
• L = Original length
• ΔT = Change in Temperature.

⇒ Make ΔT the subject of the equation

• ΔT = ΔL/(∝L)................ Equation 2

From the question,

⇒ Given:

• ∝ = 2.9×10 K⁻¹
• ΔL = 3 mm = 3×10⁻³ m
• L = 5 m

⇒ Substitute these values into equation 2

• ΔT = (3×10⁻³)/(29×5)
• ΔT = 0.003/145
• ΔT = 0.0000207 K

Hence, the change in temperature caused is 0.0000207 K

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