A brass plug is to be placed in a ring made of iron. At 20 C, the diameter of the plug is 8.723 cm and that of the inside of the ring is 8.710 cm. They must both be brought to what common temperature in order to fit? What if the plug were iron and the ring brass?

Answer:It started at 20°C, the bras and the iron must b cooled at - 150°C.

Explanation:

The formular for linear expansion is given by:

L = Lo + Lo&◇T

Where L = linear dimensions) diameter) after temperature change.

Lo=Original linear dimension

& = Coefficient of thermal expansion for the material.

◇T=Change in temperature.

At some temperature, L (brass) = L (iron)

Lo + Lo&◇T = Lo + Lo&◇T

8.753cm + 8.753cm * (8.7*10^-6C^-1) * ◇T=8.753cm + 8.753cm * (12.0*10^-6C^-1) * ◇T

8.753 + (1.636*10^-4) ◇T = 8.753 + (1.049*10^-4C^-1) ◇T

5.87 * 10^-5◇T = 0.010

◇T = 0.010 / (5.87*10^-5)

◇T = 170°C

◇T=T1-T2

T = (20 - 170) °C

T = - 150°C