Question

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 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).

Options

• 125.7°C

• 91.7°C

• 425.7°C

• 152.7°C

Answer 1

152.7°C

Explanation:

Given: initial gold ring diameter = 6.230 cm

final diameter of gold ring = diameter of bangle = 6.241 cm

`alpha = 1.4 xx 10^-5 "K"^-1`

As, `(Deltal)/l = alphaDelta"T"`

Similarly, `(Delta"D")/("D") = alphaDelta"T"`

`("D"_"final" - "D"_"initial")/("D"_"initial") = alpha("T"_"final" - "T"_"initial")`

⇒ `(6.241 - 6.230)/6.230 = 1.4 xx 10^-5("T" - 27)`

⇒ T - 27 = `0.011/6.230 xx 1/(1.4 xx 10^-5)`

⇒ T = 152.7°C