First slide

Thermal expansion

Question

A metal rod is fixed rigidly at two ends so as to prevent its thermal expansion. If L, $α$ and Y respectively denote the length of the rod, coefficient of linear thermal expansion and Young's modulus of its material, then for an increase in temperature of the rod by $∆$ T, the longitudinal stress developed in the rod is [AMU 2014]

Moderate

A

inversely proportional to $α$
B

inversely proportional to Y
C

directly proportional to $∆$ T/Y
D

independent of L

Solution

$Strain = α \cdot ∆ T \Rightarrow Stress = α Y ∆ T$
where, L = length of the rod,
$α$ = coefficient of linear thermal expansion
and Y = Young's modulus of its material.
So, the longitudinal stress developed in the rod is independent of L

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