Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

Car tires need to be inflated properly because ov…

02:19

Question

Answered step-by-step

Problem 53 Medium Difficulty

Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure $ P $ of the gas is inversely proportional to the volume $ V $ of the gas.
(a) Suppose that the pressure of a sample of air that occupies $ 0.106 m^3 at 25^{\circ} C $ is 50 kPa. Write $ V $ as a function of $ P. $
(b) Calculate $ dV\mid dP $ when $ P $ = 50 kPA. What is the meaning of the derivative? What are its units?


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Clarissa Noh
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Clarissa Noh

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

More Answers

02:31

Frank Lin

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Related Topics

Derivatives

Differentiation

Discussion

You must be signed in to discuss.
Top Calculus 1 / AB Educators
Heather Zimmers

Oregon State University

Samuel Hannah

University of Nottingham

Michael Jacobsen

Idaho State University

Joseph Lentino

Boston College

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

Video Thumbnail

44:57

Differentiation Rules - Overview

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

Join Course
Recommended Videos

0:00

Boyle's Law states th…

03:09

Boyle's Law states th…

03:34

Boyle's Law states th…

02:45

Boyle's Law The press…

00:50

Boyle's Law states th…

01:00

Boyle's Law states th…

01:21

Boyle's law Boyle…

03:54

Boyle's Law states th…

02:03

Boyle's Law states th…

03:43

Boyle's Law states th…

01:05

Boyle's law for enclo…

Watch More Solved Questions in Chapter 3

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
Problem 73
Problem 74
Problem 75
Problem 76
Problem 77
Problem 78
Problem 79
Problem 80
Problem 81
Problem 82
Problem 83
Problem 84
Problem 85
Problem 86

Video Transcript

it's clear. So when you married here. So we have PV equals K. He has a constant. We're gonna substitute 50 for P and 500.106 for ve me get Kate is equal to 5.3 and B is equal to 5.3 Overpay for part B V is equal to 5.3. Overpay p is equal to 50 Killer Paschal's. We're going to find the derivative of RV. This becomes equal to negative 5.3 he the negative to power. This could be rewritten as negative 5.3 over a piece square. Then we plug in 50 when we got negative 0.212 meters cubed over Killa Pasko's. And this represents the rate of change of the volume in respect to the pressure.

Get More Help with this Textbook
James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups
Study with other students and unlock Numerade solutions for free.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
96
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
55
Hosted by: Alonso M
See More

Related Topics

Derivatives

Differentiation

Top Calculus 1 / AB Educators
Heather Zimmers

Oregon State University

Samuel Hannah

University of Nottingham

Michael Jacobsen

Idaho State University

Joseph Lentino

Boston College

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

Video Thumbnail

44:57

Differentiation Rules - Overview

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

Join Course
Recommended Videos

0:00

Boyle's Law states that when a sample of gas is compressed at a constant temper…

03:09

Boyle's Law states that when a sample of gas is compressed at a constant pressu…

03:34

Boyle's Law states that when a sample of gas is compressed at a constant tempe…

02:45

Boyle's Law The pressure $P$ of a sample of gas is directly proportional to the…

00:50

Boyle's Law states that when a sample of gas is compressed at a constant temper…

01:00

Boyle's Law states that when a sample of gas is compressed at a constant temper…

01:21

Boyle's law Boyle's law for a certain gas states that if the temperature is con…

03:54

Boyle's Law states that when a sample of gas is compressed at a constant tempe…

02:03

Boyle's Law states that when a sample of gas is compressed at a constant tempe…

03:43

Boyle's Law states that when a sample of gas is compressed at a constant temper…

01:05

Boyle's law for enclosed gases states that if the volume is kept constant, the …
Additional Mathematics Questions

01:33

The ratio of the quantities is 5:7.If the consequent of its inverse ratio is…

02:04

Train a takes 16 hours to reach mumbai to delhi while train b takes 20 hrs t…

02:51

Find the present worth of rs. 78000 due in 4 years at 5% interest per year.<…

01:13

Two positive integers M and n are both divisible by 3, 5,15,25 and 75.find t…

01:13

Two positive integers M and n are both divisible by 3, 5,15,25 and 75.find t…

00:59

The volume of a cube is 46656 Cubic metre find the length of each side

00:59

The volume of a cube is 46656 Cubic metre find the length of each side

01:01

Find the least number which must be added to 650 to make it a perfect square…

01:08

Lalitha says that HCF and LCM of the numbers 80 and 60 are 20 and 120 respec…

01:37

for what value of x the following state ment is true 1 1/6 ×1 2/9 =11/9 × …

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started