Question 532: Thermodynamics & KTG

Question

A unit scale is to be prepared whose length does not change with temperature and remains $$20 \mathrm{~cm}$$, using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way that difference between their lengths remains constant. If length of brass is $$40 \mathrm{~cm}$$ and length of iron will be __________ $$\mathrm{cm}$$. $$\left(\alpha_{	ext {iron }}=1.2 	imes 10^{-5} \mathrm{~K}^{-1}ight.$$ and $$\left.\alpha_{	ext {brass }}=1.8 	imes 10^{-5} \mathrm{~K}^{-1}ight)$$.

Accepted Answer

$$\Delta {L_1} = {\alpha _1}{L_1}\Delta T$$
$$\Delta {L_2} = {\alpha _2}{L_2}\Delta T$$
$${\alpha _1}{L_1} = {\alpha _2}{L_2}$$
$$1.2 	imes {10^{ - 5}} 	imes {L_1} = 1.8 	imes {10^{ - 5}} 	imes {L_2}$$
$${L_1} = {{1.8} \over {1.2}} 	imes 40 = 60$$ cm

Thermodynamics & KTG

Integer / Numeric Answer Type