A uniform steel wire of cross-sectional area `0.20mm^(2) ` is held fixed by clamping its two ends. If wire is cooled from `100^(@)C` to `0^(@)C` , find
(a) temperature strain
(b) temperature stress
(c) extra force exerted by each clamp on the wire. Young's modulus of steel `=2xx10^(11)N//m^(2)` , coefficient of linear expansion of steel `=1.2xx10^(-5)//^(@)C` .

Explanation

(a) Temperature stran `in_(theta)=(DeltaL)/(L_(theta0))=alphaDeltatheta`
`=1.2xx10^(-5)xx(100-0)`
`=1.2xx10^(-3)`
(b) Temperature stress `sigma_(theta)=Yin_(theta)=YalphaDeltatheta`
`=2xx10^(11)xx1.2xx10^(-3)`
`=2.4xx10^(8)N//m^(2)`
Extra force `F=sigma_(theta)A=AYalphaDeltatheta`
`=0.2xx10^(-6)xx2.4xx10^(8)`
`=48N`