Physics For Scientists And Engineers Student Solutions Manual, Vol. 1
Physics For Scientists And Engineers Student Solutions Manual, Vol. 1
6th Edition
ISBN: 9781429203029
Author: David Mills
Publisher: W. H. Freeman
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter 20, Problem 52P

(a)

To determine

To show that LALB=αAαB .

(a)

Expert Solution
Check Mark

Explanation of Solution

Introduction:

The difference between the two lengths are constant if the length LA and LB is constant. The coefficient of linear expansions are αA and αB .

Write expression for change in length.

  ΔL=LBLA

Write expression for linear expansion.

  ΔL=(LB+αBLBΔT)(LA+αALAΔT)

Solve above expression.

  ΔL=(LBLA)+(αBLBαALA)ΔT

Substitute ΔL for LBLA in above expression and solve.

  ΔL=ΔL+(αBLBαALA)ΔT0=(αBLBαALA)ΔT0=(αBLBαALA)LALB=αBαA

Conclusion:

Thus, the equation is proved.

(b)

To determine

The value of LB .

(b)

Expert Solution
Check Mark

Explanation of Solution

Given:

The material A is brass.

The material B is steel.

The value of LA is 250cm .

Formula used:

Write expression for change in length.

  ΔL=LBLA

Write expression for linear expansion.

  ΔL=(LB+αBLBΔT)(LA+αALAΔT)

Solve above expression.

  ΔL=(LBLA)+(αBLBαALA)ΔT

Substitute ΔL for LBLA in above expression and solve.

  ΔL=ΔL+(αBLBαALA)ΔT0=(αBLBαALA)ΔT0=(αBLBαALA)

Solve above expression.

  LALB=αBαA   ..... (1)

Calculation:

Substitute 250cm for LA , 19×106K-1 for αA and 11×106K-1 for αB in equation (1).

  250cmLB=11× 10 6K -119× 10 6K -1LB=430cm

Conclusion:

Thus, the value of LB is 430cm .

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
A brass rod of length 50 cm and diameter 3.0 mm is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at 250 °C, if the original lengths are at 40.0 °C? Is there a ‘thermal stress’ developed at the junction ? The ends of the rod are free to expand (Co-efficient of linear expansion of brass = 2.0×10-5 K-1 steel =1.2×10-5 K-1
A 1.0 m * 1.5 m double-pane window consists of two 4-mm-thick layers of glass (k = 0.78 W/m·K) that are separated by a 5-mm air gap (kair = 0.025 W/m·K). The heat flow through the air gap is assumed to be by conduction. The inside and outside air temperatures are 20°C and 220°C, respectively, and the inside and outside heat transfer coefficients are 40 and 20 W/m2·K. Determine (a) the daily rate of heat loss through the window in steady operation and (b) the temperature difference across the largest thermal resistance.
Suppose due to a bad break of your femur, you require the insertion of a titanium rod to help the fracture heal. The coefficient of linear expansion for titanium is α = 8.60 × 10−6 K−1, and the length of the rod when it is in equilibrium with the leg bone and muscle at 37.0°C is 3.80 cm. How much shorter was the rod at room temperature (20.0°C)?
Knowledge Booster
Background pattern image
Physics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
University Physics Volume 2
Physics
ISBN:9781938168161
Author:OpenStax
Publisher:OpenStax
Text book image
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Heat Transfer: Crash Course Engineering #14; Author: CrashCourse;https://www.youtube.com/watch?v=YK7G6l_K6sA;License: Standard YouTube License, CC-BY