Question

A brass ring of diameter 10.00 cm at 17.8°C is heated and slipped over an aluminum rod of diameter 10.01 cm at 17.8°C. Assume the average coefficients of linear expansion are constant.

(a) To what temperature must the combination be cooled to separate the two metals?
°C
(b) Is that temperature attainable?

Yes or No    
(c) What if the aluminum rod were 9.16 cm in diameter?
°C
(d) Is that temperature attainable?

Yes or No    

Answer 1

a) at a certain point when expanding we have

Lal+dLal=Lbr+*dLbr.............1)

now we know for expansion in length

Lal+Lal*al*dT=Lbr+Lbr*br*dT

on rearranging we have

dT=Lal-Lbr/Lbr*Br-Lal*al...........2)

dT=10.01-10.00/10*19*10^-6-10.01*24*10^-6=-199^oC

17.8-199=-181.2^o C  

so answer is -181.2^o C or -181⁰ C

b) since its less than absolute zero temperture so yes its attainable

c) using eqn 2) we have for new dia

dT=9.16-10.00/10*19*10^-6-24*10^-6*9.16=28150 ^oC

so answer is 28150^o C

d) No, this temperature is too high.