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10-1.Thermometry, Thermal Expansion and Calorimetry
medium
Coefficient of linear expansion of brass and steel rods are $\alpha_1$ and $\alpha_2$. Lengths of brass and steel rods are $l_1$ and $l_2$ respectively. If $\left(l_2-l_1\right)$ is maintained same at all temperatures, which one of the following relations holds good?
A
${ \alpha _1}{l_2}^2 = \;{ \alpha _2}{l_1}^2$
B
${ \alpha_1}^2{l_2} =\;\;{ \alpha_2}^2 {l_1}$
C
${ \alpha _1} {l_1} ={ \alpha _2} {l_2}$
D
${ \alpha_1} {l_2}={ \alpha _2} {l_1}$
(NEET-2016) (AIPMT-1999)
Solution
$L_{1}=l_{1}\left(1+\alpha_{1} \Delta T\right)$
$L_{2}=l_{2}\left(1+\alpha_{2} \Delta T\right)$
$L_{1}-L_{2}=l_{1}-l_{2}+\Delta T \left(l_{1} \alpha_{1}-l_{2} \alpha_{2}\right)$
For difference to remain same
$\alpha_{1} l_{1}-\alpha_{2} l_{2}=0$
$ \alpha_{1} l_{1}=\alpha_{2} l_{2}$
Standard 11
Physics
