A steel bar (E = 200E = 200, α = 12 × 10 − 6/°C) expands by 0.3 mm due to  a temperature increase. If the original length of the bar was 15 cm, what was the temperature rise?

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  1. 166.6°C
  2. 100°C
  3. 180°C
  4. 120.6°C

Answer (Detailed Solution Below)

Option 1 : 166.6°C
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Detailed Solution

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Explanation:

Thermal Expansion of a Steel Bar

  • Thermal expansion refers to the increase in the dimensions of a material when it is subjected to a temperature rise. For a linear material like a steel bar, this expansion can be calculated using the coefficient of linear expansion.

Given Data:

  • Coefficient of linear expansion (α) = 12 × 10−6/°C
  • Original length of the steel bar (L0) = 15 cm = 150 mm
  • Expansion of the bar (ΔL) = 0.3 mm

Formula:

The formula for linear expansion is given by:

ΔL = α × L0 × ΔT

Where:

  • ΔL = Change in length (0.3 mm)
  • α = Coefficient of linear expansion (12 × 10−6/°C)
  • L0 = Original length (150 mm)
  • ΔT = Change in temperature (°C)

Calculation:

Rearranging the formula to solve for ΔT:

ΔT = ΔL / (α × L0)

Substituting the given values:

ΔT = 0.3 / (12 × 10−6 × 150)

ΔT = 0.3 / (1.8 × 10−3)

ΔT = 166.67 °C

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