Thermal Expansion Problem: Help Solve Clearance Issue

[kris24tf]

Thermal Expansion Please Help!

I have a Thermal Expansion problem that I am having trouble with...

It goes :

A brass rod has a circular cross section of radius .5 cm. The rod fits into a circular hole in a copper sheet with a clearance of .010 mm completely around it when both it and the sheet are at 20 degrees C. At what temperature will the clearance be zero?

I know I have to use Area of Expansion here, but I am not sure which version to use. I knwo to convert .5 cm to .005m and .010mm to 10m. I also know that delta T equals T-293=20-293=-273K. I do not know how to develop the equation. Any assistance would be appreciated, although I will warn that I do not do well with written explanations as well as numerical ones...

 

[member 553083]

Thank you! The equation for the thermal expansion of an object with a circular cross section is:Δx = α(T−T₀)Rwhere α is the coefficient of linear expansion, T is the temperature of the object, T₀ is the initial temperature, and R is the radius of the circular cross section. Using the given values, we can solve for T:0.010 mm = α(T−293)0.005 mT = 293 + (0.010 mm / (α 0.005 m))T = 293 + (10 x 10^-3 m / (α 0.005 m))T = 293 + (20 x 10^-3 m / α)Therefore, the temperature at which the clearance will be zero is 293 + (20 x 10^-3 m / α), where α is the coefficient of linear expansion for brass and copper.