(a) Answer The temperature change in degree per inch for the gypsum wallboard is − 3.75 degree/inch . Explanation Given information: The given figure is as follows. Calculation: The formula to calculate the temperature change is given by, Δ t = Δ y Δ x . Find the temperature change in degree per inch for the gypsum wallboard as follows. Δ t = 68 − 69.5 0.4 − 0 = − 1.5 0.4 = − 3.75 degree/inch Therefore, the temperature change in degree per inch for the gypsum wallboard is − 3.75 degree/inch . (b) To determine To find: The temperature change in degree per inch for the fiberglass insulation. Answer The temperature change in degree per inch for the fiberglass insulation is − 16.1 degree/inch . Explanation Given information: The given figure is as follows. Calculation: The formula to calculate the temperature change is given by, Δ t = Δ y Δ x . Find the temperature change in degree per inch for the gypsum wallboard as follows. Δ t = 9 − 68 4 − 0.4 = − 59 3.6 = − 16.1 degree/inch Therefore, the temperature change in degree per inch for the fiberglass insulation is − 16.1 degree/inch . (c) To determine To find: The temperature change in degree per inch for the wood sheathing. Answer The temperature change in degree per inch for the wood sheathing is − 7.1 degree/inch . Explanation Given information: The given figure is as follows. Calculation: The formula to calculate the temperature change is given by, Δ t = Δ y Δ x . Find the temperature change in degree per inch for the wood sheathing as follows. Δ t = 4 − 9 4.7 − 4 = − 5 0.7 = − 7.1 degree/inch Therefore, the temperature change in degree per inch for the wood sheathing is − 7.1 degree/inch . (d) To determine To find: The best and poorest insulating material. Answer The best insulator is fiberglass insulation and poorest insulator is Gypsum wallboard. Explanation Given information: The given figure is as follows. The best insulating material will have the highest temperature change per inch, because that will allow larger temperature difference on opposite sides of thinner layers. From the above calculation, it can be concluded that the fiberglass insulation has highest temperature change so it will be best insulator. The Gypsum wallboard has lowest temperature change so it will be poorest insulator. Therefore, the temperature change in degree per inch for the wood sheathing is − 7.1 degree/inch .

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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Question

Chapter 1.1, Problem 42E

(a)

To determine

To find: The temperature change in degree per inch for the gypsum wallboard.

(a)

Expert Solution

Answer to Problem 42E

The temperature change in degree per inch for the gypsum wallboard is −3.75 degree/inch .

Explanation of Solution

Given information: The given figure is as follows.

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 1.1, Problem 42E , additional homework tip 1

Calculation:

The formula to calculate the temperature change is given by, Δt=ΔyΔx .

Find the temperature change in degree per inch for the gypsum wallboard as follows.

Δt=68−69.50.4−0=−1.50.4=−3.75 degree/inch

Therefore, the temperature change in degree per inch for the gypsum wallboard is −3.75 degree/inch .

(b)

To determine

To find: The temperature change in degree per inch for the fiberglass insulation.

(b)

Expert Solution

Answer to Problem 42E

The temperature change in degree per inch for the fiberglass insulation is −16.1 degree/inch .

Explanation of Solution

Given information: The given figure is as follows.

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 1.1, Problem 42E , additional homework tip 2

Calculation:

The formula to calculate the temperature change is given by, Δt=ΔyΔx .

Find the temperature change in degree per inch for the gypsum wallboard as follows.

Δt=9−684−0.4=−593.6=−16.1 degree/inch

Therefore, the temperature change in degree per inch for the fiberglass insulation is −16.1 degree/inch .

(c)

To determine

To find: The temperature change in degree per inch for the wood sheathing.

(c)

Expert Solution

Answer to Problem 42E

The temperature change in degree per inch for the wood sheathing is −7.1 degree/inch .

Explanation of Solution

Given information:

The given figure is as follows.

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 1.1, Problem 42E , additional homework tip 3

Calculation:

The formula to calculate the temperature change is given by, Δt=ΔyΔx .

Find the temperature change in degree per inch for the wood sheathing as follows.

Δt=4−94.7−4=−50.7=−7.1 degree/inch

Therefore, the temperature change in degree per inch for the wood sheathing is −7.1 degree/inch .

(d)

To determine

To find: The best and poorest insulating material.

(d)

Expert Solution

Answer to Problem 42E

The best insulator is fiberglass insulation and poorest insulator is Gypsum wallboard.

Explanation of Solution

Given information: The given figure is as follows.

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 1.1, Problem 42E , additional homework tip 4

The best insulating material will have the highest temperature change per inch, because that will allow larger temperature difference on opposite sides of thinner layers.

From the above calculation, it can be concluded that the fiberglass insulation has highest temperature change so it will be best insulator.

The Gypsum wallboard has lowest temperature change so it will be poorest insulator.

Therefore, the temperature change in degree per inch for the wood sheathing is −7.1 degree/inch .

Chapter 1.1, Problem 41E

Chapter 1.1, Problem 43E

Chapter 1 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

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