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 `" " = 10m^(2)`
After expansion , `A_(2) " " = 11m^(2)`
Initial temperature `T_(1) " " 90K`
Coefficient of superficial expansion = 0.0021 /K
To find : Final temperature `t_(2) = ?`
`(DeltaA)/(A) = alpha_(A) Delta_(T)`
`(A_(2)-A_(1))/(A) = alpha(T_(2)-T_(1))`
`(11-10)/(10) = 0.0021 (T_(2)-90)`
`(1)/(10xx0.0021) = T_(2)-90`
`T_(2) = (1)/(0.021)+90 = 47.6 +90 `
Final temperature, `T_(2) = 137.6 K`