   Chapter 3.5, Problem 71E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# (a) The van der Waals equation for n moles of a gas is ( p + n 2 a V 2 ) ( V − n b ) = n R T where P is the pressure. V is the volume, and T is the temperature of the gas. The constant R is the universal gas constant and a and b are positive constants that are characteristic of a particular gas. If T remains constant, use implicit differentiation to find dV/dP.(b) Find the rate of change of volume with respect to pressure of 1 mole of carbon dioxide at a volume of V = 10 Land a pressure of P = 2.5 atm. Use a = 3.592 L2-atm/ mole2 and b = 0.04267 L/mole.

(a)

To determine

To find: The derivative dVdP by implicit function.

Explanation

Given:

The equation is (P+n2aV2)(vnb)=nRT, where P is the pressure, V is the volume and T is the temperature of the gas and R, a and b are constants, T remains constant.

Derivative rules:

Chain rule: dydx=dydududx

Calculation:

Obtain the derivative the equation by using implicit differentiation.

The equation is (P+n2aV2)(vnb)=nRT.

Differentiate implicitly with respect to P,

ddx((P+n2aV2)(vnb))=ddx(nRT)

Apply the product rule and simplify the terms,

(b)

To determine

To find: The rate of change of volume with respect to pressure.

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### In Exercises 13-20, sketch a set of coordinate axes and plot each point. 19. (4.5, 4.5)

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### The difference between population variance and sample variance.

Statistics for The Behavioral Sciences (MindTap Course List)

#### Factor each expression in Problems 7-18 as a product of binomials. 7.

Mathematical Applications for the Management, Life, and Social Sciences

#### True or False: is a geometric series.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### Construct a histogram for the data in exercise 12.

Statistics for Business & Economics, Revised (MindTap Course List) 