p19_019.pdf

19. After the change in temperature the diameter of the steel rod is D s = D s 0 + α s D s 0 ∆ T and the diameter

of the brass ring is D b = D b 0 + α b D b 0 ∆ T ,where D s 0 and D b 0 are the original diameters, α s and α b are

the coecients of linear expansion, and ∆ T is the change in temperature. The rod just ﬁts through the

ring if D s = D b . This means D s 0 + α s D s 0 ∆ T = D b 0 + α b D b 0 ∆ T . Therefore,

∆ T =

D s 0 −

D b 0

α b D b 0 −

α s D s 0

3 . 000cm

−

2 . 992cm

10 − 6 / C ◦ )(3 . 000cm) = 335C ◦ .

10 − 6 / C ◦ )(2 . 992cm)

(19

−

(11

The temperature is T =25 ◦ C + 335C ◦ = 360 ◦ C.