A copper collar is to fit tightly about a steel shaft whose

A copper collar is to fit tightly about a steel shaft whose diameter is 6.006 cm at 23°C. The inside diameter of the copper collar at that temperature is 5.9800 cm. To what temperature must the copper collar be raised so that it will just slip on the steel shaft, assuming the temperature of both the steel shaft and copper collar are raised simultaneously?

Solution

k for steel = 1.3 x 10^-5

k for copper = 1.66 x 10^-5

dk = 3.6 x 10^-6

dL = (6.006 - 5.9800) = 0.026 cm

dL = L*dK*dT

L = 5.98 cm

dT = 1207.73 oC

Tf = 1207.73 + 20 = 1227.73 oC