How Hot Must the Steel Rim Be to Fit Over the Cast Iron Wheel?

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SUMMARY

The discussion centers on determining the temperature required to heat a steel rim so that it can fit over a cast iron wheel. The initial dimensions are a cast iron body with an outer diameter of 930.0 mm and a steel rim with an inner diameter of 927.0 mm at 20 degrees Celsius. Using the linear expansion formula with a coefficient of linear expansion for steel of 1.3e-5 K^-1, the calculated temperature needed for the steel rim to expand sufficiently is 268.9 degrees Celsius. Participants express skepticism about the feasibility of this temperature, considering the significant expansion required and the melting point of iron.

PREREQUISITES
  • Understanding of linear expansion principles in materials science
  • Familiarity with the coefficient of linear expansion, specifically for steel
  • Basic knowledge of thermal physics and temperature scales
  • Ability to manipulate algebraic equations for solving temperature-related problems
NEXT STEPS
  • Research the properties of materials under thermal expansion, focusing on steel and cast iron
  • Learn about the linear expansion formula and its applications in engineering
  • Investigate the melting points of various metals and their implications for thermal processing
  • Explore practical applications of thermal expansion in railway engineering and design
USEFUL FOR

This discussion is beneficial for mechanical engineers, materials scientists, and students studying thermodynamics or materials engineering, particularly those interested in the thermal properties of metals and their applications in railway systems.

Nai
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Homework Statement



The question is : Wheels for railway cars are made of a disk shaped cast iron body of outer diameter 930.0 mm and a steel rim of inner diameter 927.0 mm at 20 degrees Celsius. To what temperature must the steel rim be heated so that it will just slip over the cast iron body?

Homework Equations



I know we use the linear expansion formula which is :
The change of length=alpha(initial length)( change of temperature)
The alpha would be the coefficient of linear expansion in this case would be the steel's coefficient which is 1.3e-5 K^-1.
I don't think it's possible to get 268.9 degrees for the steel to expand o-o

The Attempt at a Solution



My work:
(930-927)=(1.3e-5)(927)(T-20)
T=268.9 degrees Celsius

I think I'm doing something wrong >___<
If anyone could help me, it would be awesome.
Thank you in advance.
 
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I don't think it's wrong. An expansion of 3mm is quite big. The answer is still far away from the melting point of iron (~ 1500 Celsius degrees)
 

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