Thermal Properties of Matter - Result Question 1
1. A copper rod of $88 cm$ and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is : $(\alpha _{Cu}=1.7 \times 10^{-5} K^{-1}.$ and $\alpha _{A 1}=2.2 \times 10^{-5} K^{-1}$ )
[2019]
(a) $6.8 cm$
(b) $113.9 cm$
(c) $88 cm$
(d) $68 cm$
Show Answer
Solution:
- (d) $l_Cu^{\prime}=l _{Cu}(1+\alpha _{Cu} \Delta T)$
$\Delta l _{Cu}=l _{Cu} \alpha _{Cu} \Delta T$
$l _{A l}^{\prime}=l _{A l}(1+\alpha _{A l} \Delta T)$
$\Delta l _{A l}=l _{A l} \alpha _{A l} \Delta T$
Since, change in length is independent of temperature
$\therefore \alpha _{Cu} l _{Cu}=\alpha _{Al} l _{Al}$
$\Rightarrow 1.7 \times 10^{-5} \times 88 cm=2.2 \times 10^{-5} \times 1 _{Al}$
$\Rightarrow l _{A l}=\frac{1.7 \times 88}{2.2}=68 cm$
