A cylindrical rod having temperature $T_1$ and $T_2$ at its end. The rate of flow of heat $Q_1$ cal/sec. If all the linear dimension are doubled keeping temperature constant, then rate of flow of heat $Q_2$ will be
- $4Q_1$
- $2Q_1$
- $\frac{Q_1}{4}$
- $\frac{Q_1}{2}$
The Correct Option is B
Solution and Explanation
When linear dimensions are double.
$A_1 \propto r^2_1, \, L_1 = L$
$A_2 \propto 4r^2_1, \, L_1 = 2L$ so $Q_2 = 2Q_1$.
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Concepts Used:
Thermal Expansion
Thermal expansion is the tendency of matter to change its shape, area, and volume in response to a change in temperature. Temperature is a monotonic function of the average molecular kinetic energy of a substance.
The expansion of the solid material is taken to be the linear expansion coefficient, as the expansion takes place in terms of height, thickness and length. The gaseous and liquid expansion takes the volume expansion coefficient. Normally, if the material is fluid, we can explain the changes in terms of volume change.
The bonding force among the molecules and atoms differs from material to material. These characteristics of the compounds and elements are known as the expansion coefficient.
