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]

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 10−5−5°C

Formula

ΔL = L1αΔT

ΔT = ^ΔL/_L1α

ΔT is the change in temperature = T₂ – T₁

T2 = ^ΔL/_L1α

+ T1

T2 = ^0.01/_100×1.2×10⁻5 + 20

T2 = 8.3 + 20

T2 = 28.3