Temperature and Length Expansion – Rankers Physics
Topic: Thermal Physics
Subtopic: Thermal Expansion

Temperature and Length Expansion

Assertion (A): Temperature of a rod is increased and again cooled to same initial temperature then its final length is equal to original length.
Reason (R): For a small temperature change, length of a rod varies as \( l = l_0 (1+\alpha \Delta T) \) provided \( \alpha \Delta T is smallĀ  \). Here symbol have their usual meaning.
 
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution:

Assertion is true as thermal expansion is reversible for elastic materials. Reason is the formula for linear expansion, \( l = l_0 (1+\alpha \Delta T) \), which confirms the assertion if \( \Delta T \) is reversed. Thus, both are true and (R) explains (A).

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