A brass rod of length 50 cm and diameter 3.0 mm is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at `250^(@)C`, if the original lengths are at `40.0^(@)C`? Is there a 'thermal stress' developed at the junction ? The ends of the rod are free to expand. Coefficient of linear expansion of brass `= 2.0 xx 10^(-5).^(@)C^(-1)` and that of steel `=1.2 xx 10^(-5).^(@)C^(-1)`.

Explanation

Let ` alpha_1 = 2 xx 10^(-5) K^(-1) , alpha_2 = 1.2 xx 10^(-5) K^(-1)`
Change in length of brass rod `Delta l_1 =alpha_1 l Delta T`
` = 2 xx 10^(-5) xx 50 (250 - 40)`
= 0.21 cm
Change in length of steel rod ` = Delta l_2 = alpha_2 l Delta T`
`= 1.2 xx 10^(-5) xx 50 (250 - 40) = 0.126 cm `
Change in length of combined rod ` = Delta l_1 + Delta l_2`
` = 0.21 + 0.126 = 0.336 cm `