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Question: The co-efficient of thermal expansion of a rod is temperature dependent and is given by the formula ...

The co-efficient of thermal expansion of a rod is temperature dependent and is given by the formula a = aT, where a is a positive constant and T in ŗC. If the length of the rod is l at temperature 0ŗC, then the temperature at which the length will be 2l is –

A

ln2α\sqrt{\frac{\mathcal{l}n2}{\alpha}}

B

ln4a\sqrt{\frac{\mathcal{l}n4}{a}}

C

1α\frac{1}{\alpha}

D

2α\frac{2}{\alpha}

Answer

ln4a\sqrt{\frac{\mathcal{l}n4}{a}}

Explanation

Solution

As; dl = a ldT \∫02ldll=a∫0TTdT\int_{0}^{2\mathcal{l}}\frac{d\mathcal{l}}{\mathcal{l}} = a\int_{0}^{T}{TdT}

ln2 = a T22\frac{T^{2}}{2}

\ T =[ln4a]1/2\left\lbrack \frac{\mathcal{l}n4}{a} \right\rbrack^{1/2}