Find the final temperature of a cooper rod. Whose area of cross section changes from `10 m^(2)` to `11m^(2)` due to heating. The copper rod is initially kept at 90K. (Coefficient of superficial expansion is 0.0021/K)

Explanation

Given: Area of copper rod `A_(0)=A_(1)=10 m^(2)`
Changes of area cross section `DeltaA=A_(2)-A_(1)`
`=11-10=1 m^(2)`
nitial temperature `t_(1)=90 K`
`Delta T=t_(2)-t_(1)`
`DeltaT=t_(2)=90`
Coefficient of superficial expansion `alpha_(A)=0.0021//K`
Then `t_(2)=?`
`alpha_(A)=(DeltaA)/(A_(0)Deltat)`
`0.0021=(1)/(10xx(t_(2)-90)) rArr t_(2)=90=(1)/(0.0021xx10)`
`t_(2)-90=(1)/(0.021)`
`t_(2)=(1)/(0.021)+90`
`t_(2)=137.6 K`