At what temperature a gold ring of diameter 6 . 230 cm be heated so that it can be fitted on a wooden bangle of diameter 6 . 241 cm ? Both the diameters have been measured at room temperature 27 ° C . (Given: coefficient of linear thermal expansion of gold α L = 1 . 4 × 10 - 5 K - 1 )

Step-by-step solution

To fit gold ring of diameter 5 . 230   cm over wooden bangle of diameter 6 . 241   cm , gold ring expansion is required. So, l = l 0 1 + α Δ T ⇒ 6 . 241 = 6 . 230 1 + 1 . 4 × 10 - 5 T - 27 ⇒ 6 . 241 6 . 230 - 1 = 1 . 4 × 10 - 5 T - 27 ⇒ T = 152 . 7 ° C