NEET Physics Question - Thermal Physics

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 \(l_0 (1 + \alpha \Delta T)\text{ for large value of }\alpha \Delta T\).

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:

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).

Rankers Physics

Thermal Expansion Formula

Solution:

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