A bimetallic strip is formed by rigidly joining a brass strip to an invar strip of…

PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

A bimetallic strip is formed by rigidly joining a brass strip to an invar strip of the same length at

25\,^{\circ}\!\text{C}

. The coefficient of linear expansion of brass is

\alpha_{1}=18\times10^{-6}\,\text{K}^{-1}

, while that of invar is

\alpha_{2}=0.9\times10^{-6}\,\text{K}^{-1}

. Each strip is

0.50\,\text{mm}

thick and

20\,\text{cm}

long. (a) Explain qualitatively why the composite strip bends when its temperature is raised. (b) Derive an expression for the radius of curvature

R

of the bent strip in terms of the common length

l

, the temperature rise

\Delta T

, and the difference in coefficients of linear expansion of the two metals. Assume the thickness of each strip is small compared to

l

and both remain perfectly elastic. (c) Calculate the numerical value of

R

when the temperature is increased by

100\,^{\circ}\!\text{C}

. (d) State two practical devices or situations where such bimetallic strips are employed and explain the role played by their differential expansion.

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