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Question: The length of a metal rod at \({{10}^{{}^\circ }}C\) is 1 m. Its coefficient of linear expansion is ...

The length of a metal rod at 10∘C{{10}^{{}^\circ }}C is 1 m. Its coefficient of linear expansion is 12×10−6/oC12\times {{10}^{-6}}{{/}^{o}}C. The temperature to which it must be heated so that the expansion in it is 12 mm is:
(A) 1000oC{{1000}^{o}}C
(B) 820oC{{820}^{o}}C
(C) 1010oC{{1010}^{o}}C
(D) 101oC{{101}^{o}}C

Explanation

Solution

We know that the ratio increases in length original length for 1 degree rise in temperature is called the coefficient of linear expansion, the ratio increases in area original area for 1 degree rise in temperature is called the coefficient of superficial expansion, and the ratio increase in volume original volume for 1 degree rise in temperature. The amount that a unit length along any direction of a substance increases for a temperature increase of one degree is called the coefficient of linear expansion of the substance. Most liquids also expand when heated.

Complete step by step answer
Let us first write that heating up a substance increases its kinetic energy. Depending on the type of expansion thermal expansion is of 3 types– Linear expansion, Area expansion and Volume expansion. The expansion of alcohol in a thermometer is one of many commonly encountered examples of thermal expansion, which is the change in size or volume of a given system as its temperature changes. The most visible example is the expansion of hot air.
We know rise in temperature is given as: change in length(initial length !!×!! coefficient of linear expansion)\dfrac{\text{change in length}}{\text{(initial length }\\!\\!\times\\!\\!\text{ coefficient of linear expansion)}}
The change in length is given as: 12 mm = 12×10−3m12\times {{10}^{-3}}m
The initial length is given as 1 m.
The value of α\alphais given as: 12×10−612\times {{10}^{-6}}
Now we have to put all the values to expect that the raise in temperature is 1000 degree centigrade.
So, the final temperature should be 1010 degree centigrade.

Hence, the correct answer is option C.

Note: We can conclude that thermal expansion is the tendency of matter to change its shape, area, volume, and density in response to a change in temperature, usually not including phase transitions. Temperature is a monotonic function of the average molecular kinetic energy of a substance. Materials expand or contract when subjected to changes in temperature. Most materials expand when they are heated, and contract when they are cooled. When free to deform, concrete will expand or contract due to fluctuations in temperature. Thermal expansion is caused when seawater expands because of the higher temperature of the water.