Question

An iron bar of length 10 m is heated from $0^0\text{C}\text{to}{100}^0\text{C}$ . If the coefficient of linear thermal expansion of iron is $\text{10}\times \text{1}{\text{0}}^{-6}{/}^0\text{C}$ the increases in the length of the bar is

• A. 0.5 cm
• B. 1.0 cm
• C. 1.5 cm
• D. 2.0 cm

Answer 1

The correct option is B 1.0 cm

The linear thermal expansion of an object can be expressed as

$\Delta l=l_0\alpha (T-T_0)$

where $\Delta l=$ change in length of the object, $l_0=$ initial length, $\alpha =$ coefficient of linear thermal expansion, $T=$ final temperature and $T_0=$ initial temperature.

So, $\Delta =10(10\times {10}^{-6})(100-0)={10}^{-2}m=1cm$