Question

A rod is found to be 200 cm long at 400C and 200.24 cm at 1000C. The coefficient of cubical expansion of the material is

Answer 1

Answer:

The formula required to calculate thermal expansion in linear manner is given as:

⇒ L = L₀ ( 1 + αΔT )

Where, L is the final length, L₀ is the initial length, α is the coefficient of linear expansion and ΔT is the change in temperature.

According to the question,

• L = 200.24 cm

• L₀ = 200 cm
• α = ?
• ΔT = 1000 - 400 = 600 °C

Substituting the values we get:

⇒ 200.24 = 200 ( 1 + α ( 600 ) )

⇒ 200.24 = 200 + 120000 (α)

⇒ 200.24 - 200 = 120000 α

⇒ 0.24 / 120000 = α

⇒ 2 × 10⁻⁶ = α

Hence the value of coefficient of linear expansion is 2 × 10⁻⁶ °C⁻¹.

Now since the question has asked for cubical (volume) expansion, we need to convert linear to volume expansion. The conversion factor is:

⇒ Volume Coefficient = 3 × Linear Coefficient

⇒ γ = 3α

Therefore coefficient of cubical expansion is: 3 × 2 × 10⁻⁶ = 6 × 10⁻⁶ °C⁻¹

Answer 2

Answer:

$\huge\fbox{ෆ╹Answer ╹ෆ}$

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$\yellow{Change in length}$ $\huge\box{ෆ╹Answer ╹ෆ}$

➳ (200.24 - 200)cm

➳ 0.24 cm

➳ 0.0024m

$\pink{So change in length = initial length x αΔT}$

Here ΔT = 60K

Initial length = 2m

Putting all the values, we get

$a = 6 \times {10}^{ - 5}$

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