Thermal Expansion of a gold ring

In summary, the problem involves a gold ring with an inner diameter of 2.26 cm getting stuck on a finger with a knuckle diameter of 2.3 cm. The temperature of the ring is 23 degrees C. To remove the ring, the temperature must be raised to a certain value. The equation used is delta L = alpha/coefficient * Lo * delta T, where delta L is the change in length, alpha is the coefficient of linear expansion, Lo is the initial length, and delta T is the change in temperature. The circumference of the ring can be found using C = pi * diameter, and in this case, it is 7.09 cm.
  • #1
thaixicedxtea
12
0

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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  • #2
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?
 
  • #3
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...
 

What is thermal expansion?

Thermal expansion is the tendency of matter to increase in volume or size when heated and decrease in volume when cooled.

How does thermal expansion affect gold rings?

Gold rings, like all materials, expand when heated and contract when cooled. This means that the ring will increase in size when heated and decrease in size when cooled.

Why is thermal expansion important to consider for gold rings?

Thermal expansion is important to consider for gold rings because it can cause the ring to change shape or even break when exposed to extreme temperature changes. This is especially important for delicate or intricate designs.

What factors affect the thermal expansion of a gold ring?

The thermal expansion of a gold ring can be affected by the type and purity of the gold, as well as the temperature and duration of exposure to heat or cold.

How can thermal expansion be managed for gold rings?

To minimize the effects of thermal expansion on a gold ring, it is important to choose a high-quality gold that is less prone to changes in temperature and to avoid exposing the ring to extreme temperatures. Additionally, it is important to properly store the ring and avoid sudden temperature changes.

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