Solving Expanding Problem with Iron and Aluminium Cylinders

[Skipe_]

I may write a bit rubbish English since it's not my native language but please ask if something sounds wrong or hard to understand.

Homework Statement

The inner diameter of an iron cylinder is 80,00 mm (millimeter) and the inner diameter of an aluminium cylinder located inside this iron cylinder is 79,80 mm. The temperature is 20*C. In which temperature the aluminium cylinder jams to the iron cylinder? I have tried to solve this multiple times yet never succeeded. How should I proceed?

Homework Equations

I'm pretty confident this'd be solved by the expanding of volume V=V₀(1+$$\gamma$$$$\Delta$$V)

The Attempt at a Solution

Haven't had any potential attempts so I'll leave this blank.

 

[Delphi51]

I would use the linear expansion of the diameters. I don't think it matters that one is hollow because its circumference still expands at the same rate. Do you have the coefficients of expansion for the two metals?

 

[srmeier]

I may write a bit rubbish English since it's not my native language but please ask if something sounds wrong or hard to understand.

Homework Statement

The inner diameter of an iron cylinder is 80,00 mm (millimeter) and the inner diameter of an aluminium cylinder located inside this iron cylinder is 79,80 mm. The temperature is 20*C. In which temperature the aluminium cylinder jams to the iron cylinder? I have tried to solve this multiple times yet never succeeded. How should I proceed?

Homework Equations

I'm pretty confident this'd be solved by the expanding of volume V=V₀(1+$$\gamma$$$$\Delta$$V)

The Attempt at a Solution

Haven't had any potential attempts so I'll leave this blank.

If I understand you correctly, the aluminum cylinder is inside of the iron cylinder. The iron cylinder has a initial radius and the aluminum cylinder has an outter radius. Things are comfy at 20c and we want to increase the temp, allowing the aluminum cylinder to jam with the iron cylinder (assuming $$\gamma_(aluminum) > \gamma_(iron)$$).

$$V=\pi r^2 L$$
$$\pi r_f^2 L=\pi r_i^2 L (1+ \gamma [T_f-T_i])$$

because L (the length of the cylinder) reduces to one it is not given (assuming the expansion in their lengths is negligible compared to the expansion in their radii). The situation we are concerned with is when $$r_f$$ is the same for both cylinders. Therefore, set the equations equal to each other and solve for $$T_f$$