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) $68 cm$

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Solution:

  1. (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

$\therefore \alpha _{Cu} l _{Cu}=\alpha _{Al} l _{Al}$

$\Rightarrow 1.7 \times 10^{-5} \times 88 cm=2.2 \times 10^{-5} \times 1 _{Al}$

$\Rightarrow l _{A l}=\frac{1.7 \times 88}{2.2}=68 cm$