# Theaverage rate of change of P as V increase from 200 in 3 to 250 in 3 .

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 2, Problem 28RE

(a)

To determine

## To find:Theaverage rate of change of P as V increase from 200 in3 to 250 in3 .

Expert Solution

The average rate of change of P as V increase from 200in3 to 250in30.016lb/in2/in3 .

### Explanation of Solution

Given information:

For acertain gas PV=800 .

Where P is the pressure and V is the volume.

Calculation:

For acertain gas PV=800 .

PV=800P=800Vf(V)=800V

Calculate the average rate of change of P and V from 200in3 to 250in3 .

ΔPΔV=f(250)f(200)250200=80025080020050=3.2450=0.850=0.016lb/in2/in3

Therefore, the average rate of change of P as V increase from 200in3 to 250in3

0.016lb/in2/in3 .

(b)

To determine

### To find:The instantaneous rate of change of V with respect to P .

Expert Solution

The instantaneous rate of change of V with respect to P is inversely proportional to the square of P .

### Explanation of Solution

Given information:

For acertain gas PV=800 .

Where P is the pressure and V is the volume.

Calculation:

The value of V is.

PV=800V=800P

Calculate instantaneous rate of change of V with respect to P .

ΔV=ddP(800P)=800(p2)=800p2

From the above equation, the instantaneous rate of change of V with respect to P is inversely proportional to the square of P .

Therefore, the instantaneous rate of change of V with respect to P is inversely proportional to the square of P .

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