When a metal rod is heated, its atoms gain kinetic energy and vibrate more vigorously. As they vibrate, they tend to move slightly further apart because the increased energy weakens the attractive forces that hold them at a fixed distance. This increased atomic spacing results in the rod expanding in size.
Thus, the expansion of the metal rod occurs because the distance among its atoms increases with temperature. This phenomenon is the essence of thermal expansion.
The percentage change in length of 1 m iron rod if its temperature changes by 100ºC is (\(\alpha\) for iron is \(2 \times 10^{-5}/\text{ºC}\))
The percentage change in length is given by \(\frac{\Delta L}{L} \times 100 = \alpha \Delta T \times 100 = (2 \times 10^{-5}) \times 100 \times 100 = 0.2%\).
Thin copper wire of length \( L \) increases in length by 2% when heated from \( T_1 \) to \( T_2 \). If a copper cube having side \( 10L \) is heated from \( T_1 \) to \( T_2 \) then the percentage change in volume of the cube is
The percentage change in length is \( \frac{\Delta L}{L} \times 100 = 2% \). Since volume expansion coefficient is three times the linear expansion coefficient (\( \gamma = 3\alpha \)), the percentage change in volume is \( 3 \times 2% = 6% \).
The percentage change in length of \( 1\text{ m} \) iron rod if its temperature changes by \( 100^circ\text{C} \) is (\( \alpha \) for iron is \( 2 \times 10^{-5}/^circ\text{C} \))
Using the formula for thermal expansion, \( \frac{\Delta L}{L} \times 100 = \alpha \Delta T \times 100 \). Plugging in the values: \( 2 \times 10^{-5} \times 100 \times 100 = 0.2% \).
Assertion (A): Water is considered unsuitable for use in thermometers.
Reason (R): Thermal Expansion of water is non-uniform.
Assertion (A) is true. Water exhibits anomalous expansion between \(0^{\circ}\text{C}\) and \(4^{\circ}\text{C}\), making it unreliable for linear temperature scales. Reason (R) is true.
The non-uniform thermal expansion of water (especially its contraction then expansion) is why it's unsuitable for thermometers. (R) is the correct explanation for (A).
Assertion (A): The temperature of a metallic rod is raised by a temperature \(\Delta t\) so that its length becomes double. The value of \(\alpha\) (coefficient of linear expansion) is given by \(\frac{\log_e (2)}{\Delta t}\).
Reason (R): Coefficient of linear expansion is defined as \(\frac{1}{l} \frac{dl}{dt}\).
Reason (R) is the correct definition for the instantaneous coefficient of linear expansion (assuming \(t\) is temperature), so it is true. Integrating \(dl/l = \alpha dT\) with constant \(\alpha\) gives \(ln(l/l_0) = \alpha \Delta T\), so \(l = l_0 e^{\alpha \Delta T}\). If \(l = 2l_0\), then \(2 = e^{\alpha \Delta T}\), leading to \(\alpha = \frac{ln 2}{\Delta T}\).
So Assertion (A) is true. (R) provides the foundational definition from which (A) is derived, thus it's the correct explanation.
Assertion (A): Liquids usually expand more than solids.
Reason (R): The intermolecular forces in liquids are weaker than in solids.
Assertion (A) is true as liquids typically have higher coefficients of thermal expansion than solids. Reason (R) is true because weaker intermolecular forces in liquids allow molecules to move more freely and separate further upon heating.
(R) correctly explains (A), as the weaker forces enable greater thermal 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 \( \alpha \Delta T is small \). Here symbol have their usual meaning.
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).