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
Verified Correct Answer: C.
Physical Principles & Numerical Solution
GIVEN DATA:
where \DeltaL is the increase in length = 0.01
L1 is the initial length = 100
T1 = 20
T2 = ?
\alpha is the linear expansivity of iron = 1.2 x 10\(^{-5}\)^\circC
Formula
\DeltaL = L1\alpha\DeltaT
\DeltaT = \(\frac{\DeltaL}{L1\alpha}\)
\DeltaT is the change in temperature = T2 - T1
T2 = \(\frac{\DeltaL}{L1\alpha}\) + T1
T2 = \(\frac{0.01}{100 \times 1.2 x 10^{-5}}\) + 20
T2 = 8.3 + 20
T2 = 28.3
Source: WAEC / JAMB / NECO Classroom Archive (Record #59417)