The Length Of An Iron Bar Is 100cm At 20°C. At What Temperature Will Its Length Increase By [Linear Expansivity Of Iron = 1.2 X 10^−5°C]

A. 48.0°C
B. 38.0°C
C. 28.3°C
D. 23.0°C

Correct Answer:

Option C = 28.3°C

Explanation

GIVEN DATA:

where ΔL is the increase in length = 0.01

L1 is the initial length = 100

T1 = 20

T2 = ?

α is the linear expansivity of iron = 1.2 x 10 $^{- 5}$ °C

Formula

ΔL = L1αΔT

ΔT = $\frac{Δ L}{L 1 α}$

ΔT is the change in temperature = T₂– T₁

T2 = $\frac{Δ L}{L 1 α}$

+ T1

T2 = ^{$\frac{0.01}{100 \times 1.2 x 10^{- 5}}$}/_100×1.2×10⁻5 + 20

T2 = 8.3 + 20

T2 = 28.3

The length of an iron bar is 100cm at 20°C. At what temperature will its length increase by 0.01%? [Linear expansivity of iron = 1.2 x 10^−5°C]