http://www.adamsavenuedesign.com/brass-marble/
Linear and volumetric thermal expansion!?
I'm really struggling with this question:
A glass marble of diameter 0.01m rests at 0 Celsius in a circular hole in a brass plate, the hole having diameter 0.009995m. Calculate the temperature of the assembly at which the marble falls through the hole.
linear expansivity of glass = 8*10^-6 K^-1
linear expansivity of brass = 18*10^-6 K^-1
I'd really appreciate any help anyone can give me on this please. Thanks!
Key 1 : marble falls through the hole when both area i.e. Area of Hole and Marble are equal.
Key 2: At = Ao(1+bt)
Where At = Area @ temp t; Ao = Area @ 0 degree; b=Coefficient of Superficial (Surface) expansion
Key 3: As Coefficient of linear expansion (a) is given we need to calculate Coefficient of superficial expansion (b). And the relation is b=2a
Hence;
Aoh(1+bt) = Aog(1+bt)
Aoh= Area of hole at 0 degree
Aog = Area of Glass at 0 degree
So
Aoh(1+2at) = Aog(1+2at)
0.009995(1+2*18*10^-6 t) = 0.01(1+8*10^-6 t)
Solve for t. you get t = 17.85 Degree ( App )
Check my calculation but the idea is this.
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