Question

A hot wire of copper is stretched at a temperature of ${150}^{\circ }C$ between two fixed walls. At what temperature will the wire break when it is cooled? The breaking stress of copper is $2.45\times {10}^{8}N/m^2$. Young's modulus of copper $=11.8\times {10}^{10}N/m^2$, coefficient of linear expansion of copper $=1.6\times {10}^{-5}{/}^{\circ }C$.

• A. ${20.2}^{\circ }C$
• B. ${43.2}^{\circ }C$
• C. ${64.9}^{\circ }C$
• D. ${70.2}^{\circ }C$

Answer 1

Answer: (A)

${20.2}^{\circ }C$

Breaking stress $=2.45\times {10}^{8}N/m^2$

$Y=11.8\times {10}^{10}N/m^2\alpha =1.6\times {10}^{-5}{/}^{o}C$

Now, $Y=\frac{Stress}{Strain}$

Putting values

$Strain=\frac{Stress}{Y}=\frac{2.45\times {10}^8}{1.6\times {10}^{-5}}=0.21\times {10}^{-2}$

$strain=\frac{△l}{l}=\alpha △T$

So,

$\alpha △T=0.21\times {10}^{-2}1.6\times {10}^{-5}△T=0.21\times {10}^{-2}△T=0.129\times {10}^3℃=129.7℃T=150-129.7T\simeq 20.2℃$

At this temperature, the wire will break when it is cooled.