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 αL = 1.4 × 10–5 K–1)
(Given: coefficient of linear thermal expansion of gold αL = 1.4 × 10–5 K–1)
- 125.7°C
- 91.7°C
- 425.7°C
- 152.7°C
The Correct Option is A
Solution and Explanation
The correct answer is (D) : 152.7°C
\(ΔD = DαΔT\)
\(ΔT = \frac{0.011}{6.230 × 1.4 × 10^{-5}}\)
= 126.11°C
\(⇒ T_f = T + ΔT\)
= (27 + 126.11)°C
= 153.11°C
Therefore , 153.11 is nearest to the 152.7
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Concepts Used:
Thermal Expansion
Thermal expansion is the tendency of matter to change its shape, area, and volume in response to a change in temperature. Temperature is a monotonic function of the average molecular kinetic energy of a substance.
The expansion of the solid material is taken to be the linear expansion coefficient, as the expansion takes place in terms of height, thickness and length. The gaseous and liquid expansion takes the volume expansion coefficient. Normally, if the material is fluid, we can explain the changes in terms of volume change.
The bonding force among the molecules and atoms differs from material to material. These characteristics of the compounds and elements are known as the expansion coefficient.
