Thermal Expansion of a gold ring

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SUMMARY

The discussion focuses on calculating the temperature required to expand a gold ring with an inner diameter of 2.26 cm to fit over a knuckle with a diameter of 2.3 cm. The coefficient of linear expansion for gold is specified as 1.42 x 10-5 per degree Celsius. Using the formula for linear expansion, delta L = α * L0 * delta T, participants clarify that the initial length (L0) can be derived from the circumference of the ring, calculated as 7.09 cm. The goal is to determine the necessary temperature increase to achieve this expansion.

PREREQUISITES
  • Understanding of linear expansion and its formula.
  • Knowledge of the coefficient of linear expansion, specifically for gold.
  • Ability to calculate circumference from diameter using C = π * d.
  • Basic algebra skills for manipulating equations.
NEXT STEPS
  • Calculate the required temperature increase using the linear expansion formula.
  • Explore the properties of thermal expansion in different materials.
  • Learn about the practical applications of thermal expansion in engineering.
  • Investigate the effects of temperature on the physical properties of metals.
USEFUL FOR

Students studying physics, particularly those focusing on thermal expansion, as well as engineers and jewelers interested in material properties and applications related to temperature changes.

thaixicedxtea
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Homework Statement


You somehow manage to get a gold ring with inner diameter 2.26 cm stuck on your finger, even though your knuckle has a diameter of 2.3 cm. The temperature of the ring is 23 degrees C.
To what temperature would you have to heat the ring in order to get it off your finger? The coefficient of linear expansion of gold is 1.42 E -5. Answer in units of C.


Homework Equations


delta L = alpha/coefficient * Lo * delta T



The Attempt at a Solution


Since I'm given the linear expansion coefficient, I figured that I'm going to use the delta L equation. What I'm stuck with is what to do with the diameters given, like how do I figure out the initial length from the diameter...
 
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thaixicedxtea said:

Homework Statement


You somehow manage to get a gold ring with inner diameter 2.26 cm stuck on your finger, even though your knuckle has a diameter of 2.3 cm. The temperature of the ring is 23 degrees C.
To what temperature would you have to heat the ring in order to get it off your finger? The coefficient of linear expansion of gold is 1.42 E -5. Answer in units of C.


Homework Equations


delta L = alpha/coefficient * Lo * delta T



The Attempt at a Solution


Since I'm given the linear expansion coefficient, I figured that I'm going to use the delta L equation. What I'm stuck with is what to do with the diameters given, like how do I figure out the initial length from the diameter...

What is the circumference of the ring?
 
C equals pi * diameter, so the circumference of the ring is 2.26 cm * pi = 7.09.
Is that the length? If it is, why?
I must be thinking too hard...
 

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