Question

A thin silver wire has length $L=18 \mathrm{~cm}$ when the temperature is $T=30^{\circ} \mathrm{C}$. Estimate $\Delta L$ when $T$ decreases to $25^{\circ} \mathrm{C}$ if the coefficient of thermal expansion is $k=1.9 \times 10^{-5 \circ} \mathrm{C}^{-1}$ (see Example 3).

   A thin silver wire has length $L=18 \mathrm{~cm}$ when the temperature is $T=30^{\circ} \mathrm{C}$. Estimate $\Delta L$ when $T$ decreases to $25^{\circ} \mathrm{C}$ if the coefficient of thermal expansion is $k=1.9 \times 10^{-5 \circ} \mathrm{C}^{-1}$ (see Example 3).
Show more…
Calculus
Calculus
Jon Rogawski,… 2nd Edition
Chapter 4, Problem 31 ↓
AceChat toggle button
Close icon
Ace pointing down

Please give Ace some feedback

Your feedback will help us improve your experience

Thumb up icon Thumb down icon
Thanks for your feedback!
Profile picture
A thin silver wire has length $L=18 \mathrm{~cm}$ when the temperature is $T=30^{\circ} \mathrm{C}$. Estimate $\Delta L$ when $T$ decreases to $25^{\circ} \mathrm{C}$ if the coefficient of thermal expansion is $k=1.9 \times 10^{-5 \circ} \mathrm{C}^{-1}$ (see Example 3).
Close icon
Play audio
Feedback
Powered by NumerAI
Kathleen Carty Ivan Kochetkov
David Collins verified

Lucas Finney and 95 other educators are ready to help you.

Ask a new question

*

Labs

-

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

*

Recommended Videos

-
a-thin-silver-wire-has-length-l18-mathrmcm-when-the-temperature-is-t30circ-mathrmc-estimate-delta--3

A thin silver wire has length $L=18 \mathrm{~cm}$ when the temperature is $T=30^{\circ} \mathrm{C}$. Estimate $\Delta L$ when $T$ decreases to $25^{\circ} \mathrm{C}$ if the coefficient of thermal expansion is $k=1.9 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$ (see Example 6 ).

Calculus: Early Transcendentals

Applications of the Derivative

Linear Approximation and Applications

a-thin-silver-wire-has-length-l18-mathrmcm-when-the-temperature-is-t30circ-mathrmc-estimate-delta-l-

A thin silver wire has length $L=18 \mathrm{cm}$ when the temperature is $T=30^{\circ} \mathrm{C} .$ Estimate $\Delta L$ when $T$ decreases to $25^{\circ} \mathrm{C}$ if the coefficient of thermal expansion is $k=1.9 \times 10^{-1}($ see Example 3$)$ .

Calculus for AP

APPLICATIONS OF THE DERIVATIVE

Linear Approximation and Applications

a-gold-wire-20-mathrmm-long-has-its-temperature-lowered-by-250-circ-mathrmc-assume-the-linear-coeffi

A gold wire $20 \mathrm{~m}$ long has its temperature lowered by $25.0{ }^{\circ} \mathrm{C}$. Assume the linear coefficient of expansion is constant over that range of temperatures. Calculate the change in length of the wire. [Hint: Use Table 15-1.]

Schaum’s Outline of College Physics


*

Transcript

-
00:01 For this problem, we are told that a thin silver wire has length l equals 18 centimeters when the temperature is 30 degrees celsius.
00:08 We are asked to estimate delta l when t decreases to 25 degrees celsius if the coefficient of thermal expansion is k equals 1 .9 times 10 to negative 5 degrees celsius inverse.
00:22 So to begin, we have that dl by dt equals kl, and we can then say that, dl is going to equal dl by dt, that should be a capital t temperature, dl by dt times dt.
00:40 So what we need to do is figure out the derivative with respect to temperature and multiply it by the change in temperature.
00:48 So we have then that dl by dt, you need to figure out here, dl by dt when t equals 30 is going to equal 1 .9 times 10 to the negative 5 times the length, which is 18.
01:10 So we have that's degree celsius inverse, and then we multiply by 18 centimeters...
Need help? Use Ace
Ace is your personal tutor. It breaks down any question with clear steps so you can learn.
Start Using Ace
Ace is your personal tutor for learning
Step-by-step explanations
Instant summaries
Summarize YouTube videos
Understand textbook images or PDFs
Study tools like quizzes and flashcards
Listen to your notes as a podcast
Continue solving this problem
Create a free account to:
  • View full step-by-step solution
  • Ask follow-up questions with Ace AI
  • Save progress and study later
Continue Free
Join the community

18,000,000+

Students on Numerade


Trusted by students at 8,000+ universities

Numerade

Get step-by-step video solution
from top educators

Continue with Clever
or



By creating an account, you agree to the Terms of Service and Privacy Policy
Already have an account? Log In

A free answer
just for you

Watch the video solution with this free unlock.

Numerade

Log in to watch this video
...and 100,000,000 more!


EMAIL

PASSWORD

OR
Continue with Clever