You have a brass ring of inside diameter 10.00 cm that is at 20.0 o C. You want to slip this ring over an aluminum rod that is at 20.0 o C and has a diameter of 10.01 cm. a. To what temperature do you have to heat the ring to slip it over the rod? b. Once you have the ring over the rod they are allowed to cool back to room temperature (20.0 o C). To what temperature must the combination be cooled to separate the two metals? c. If the diameter of the rod was 10.02 cm would you still be able to get the brass ring off? Solution a) coefficient of expansion for brass ? b = 1.9e-5 / degree celsius for aluminium, ? a = 2.4e-5 / degree celsius T = T o + d a - d b / d b ? b T = 20 + 10.01 - 10 / 10.01*2.4e-5 T = 72.632 degree celsius b) T = d a - d b / d b ? b - d a ? a T = 10.01 - 10 / 1.9E-4 - 2.402E-4 T = - 199.203 T = - 199.203 + 20 = -179.203 degree celsius c) for d a = 10.02 , T = + 20 - 378.40 = 358.4 . This is not possible as we cannot go below absolute zero .

1. You have a brass ring of inside diameter 10.00 cm that is at 20.0 o
C. You want to slip this ring
over an aluminum rod that is at 20.0 o
C and has a diameter of 10.01 cm.
a. To what temperature do you have to heat the ring to slip it over the rod?
b. Once you have the ring over the rod they are allowed to cool back to room temperature (20.0 o
C). To what temperature must the combination be cooled to separate the two metals?
c. If the diameter of the rod was 10.02 cm would you still be able to get the brass ring off?
Solution
a) coefficient of expansion for brass ? b = 1.9e-5 / degree celsius
for aluminium, ? a = 2.4e-5 / degree celsius
T = T o + d a - d b / d b ? b
T = 20 + 10.01 - 10 / 10.01*2.4e-5
T = 72.632 degree celsius
b) T = d a - d b / d b ? b - d a ? a
T = 10.01 - 10 / 1.9E-4 - 2.402E-4
T = - 199.203
T = - 199.203 + 20 = -179.203 degree celsius
c) for d a = 10.02 , T = + 20 - 378.40 = 358.4 . This is not possible as we cannot go below
absolute zero