Question

If $\alpha$ denotes the coefficient of linear expansion of a block , $L$ denotes length of the block and $T$ denotes temperature, then which one of the following options is true?

• A. $dL-\alpha LdT=0$
• B. $dL+\alpha LdT=0$
• C. $\alpha dL-LdT=0$
• D. $\alpha dL+LdT=0$

Answer 1

The correct option is A $dL-\alpha LdT=0$

From the definition of linear expansion,
$\alpha =\left(\frac{1}{L}\right)\left(\frac{dL}{dT}\right)$
$\Rightarrow \alpha LdT=dL$
$\Rightarrow$$dL-\alpha LdT=0$
Hence, option (a) is the correct answer.