Question

Chapter 12, Problem 012

The Eiffel Tower is a steel structure whose height increases by 19.1 cm when the temperature changes from -9 to +41 ^oC. What is the approximate height (in meters) at the lower temperature?

Chapter 12, Problem 014

A commonly used method of fastening one part to another part is called "shrink fitting." A steel rod has a diameter of 2.0044 cm, and a flat plate contains a hole whose diameter is 2.0000 cm. The rod is cooled so that it just fits into the hole. When the rod warms up, the enormous thermal stress exerted by the plate holds the rod securely to the plate. By how many Celsius degrees should the rod be cooled?

Chapter 12, Problem 029

Interactive Solution 12.29 presents a model for solving problems of this type. A thin spherical shell of silver has an inner radius of 5.94 x 10^-2 m when the temperature is 27.1 °C. The shell is heated to 144 °C. Find the change in the interior volume of the shell.

Answer 1

Problem 012

ΔL = α*Lo*ΔT

ΔT = 41-(-9) = 50 ^oC

α = linear expansion coefficient = 0.000012 / ^oC for steel

ΔL= 0.191

Hence Lo = ΔL  / α*ΔT

= 0.191 / (0.000012*50)

= 318.33 m --> Answer

Problem 14:-

ΔL = α*Lo*ΔT

Written in terms of diameter d of the rod

Δd = α*do*ΔT

ΔT = Δd / α*do

Here

Δd =  2.0044 cm - 2.0000 cm = 0.0044 cm

α = linear expansion coefficient = 0.000012 / ^oC for steel

do =  2.0044 cm

Hence ΔT = Δd / α*do

= 0.0044 cm / (0.000012*2.0044 cm)

= 182.9 ^oC = 183 ^oC  --> Answer