Thermal Expansion: Practice Problem & Solution
Assertion (A): The expanded length l of a rod of original length l_0 is not correctly given by assuming \(\alpha\) to be constant with T \( \l = \l_0 (1 + \alpha \Delta T)\), if \(\alpha \Delta T\) is large. Reason (R): It is given by \(l = \l_0 \text{e}^{\alpha \Delta T}\), which cannot be treated as being approximately equal to \(l_0 (1 + \alpha \Delta T)\text{ for large value of }\alpha \Delta T\).
Solution Explained:
To solve this problem, we apply the core principles of Thermal Expansion. Understanding the underlying formula is key to arriving at the correct answer below:
The standard linear expansion formula \(ell = \ell_0 (1 + \alpha \Delta T)\text{ is an approximation valid for small }\alpha \Delta T\), derived from the exponential form \(ell = \ell_0 \text{e}^{\alpha \Delta T}\). If \(alpha \Delta T\) is large, this approximation fails. Both (A) and (R) are true, and (R) correctly explains (A).
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