Question

The coefficient of linear expansion of copper is $$17\times {10}^{-6}$$ C. A copper statue is 93 m tall on the summer morning of temperature $${25}^{0}C$$. What is the maximum order of increase in magnitude of the height in the statue (maximum temperature of day is ${45}^{0}C$ ).

Answer 1

Hint: The expansion means, change or increase in length. If the change in length is along one dimension (length) over the volume, then it is called linear expansion. Now, we will assume that the effect of pressure is negligible, then the coefficient of linear expansion is the rate of change of unit length per unit degree change in temperature. The coefficient of linear expansion can be mathematically written as:
 $\mathrm{\Delta }l=l\alpha \mathrm{\Delta }T$
 where,
 $$\alpha$$ is the coefficient of linear expansion.
 $\mathrm{\Delta }l$ is the unit change in length.
 $\mathrm{\Delta }T$ is the unit change in temperature.

Complete step-by-step answer
Here, first we will use the formula $$\mathrm{\Delta }l=l\alpha \mathrm{\Delta }T$$ to calculate the change in length of the copper statue.
 $\mathrm{\Delta }l=93\times 17\times {10}^{-6}\times (45-25)$
So,
 $\mathrm{\Delta }l=100mm$

Hence, the maximum order of increase in magnitude of the height in statue is 100mm that is option D

Additional information: The linear expansion coefficient is an intrinsic property of every material. Hence, it varies from one material to another. The rate at which a material expands purely depends on the cohesive force between the atoms. Cohesive force is the force that binds two or more atoms. In other words, the cohesive force resists the separation between the atoms.

Note: One thing to be Note:d is that the effect of pressure on coefficient of linear expansion is negligible and the final answer should be in the order of hundred.