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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

In a steam engine the pressure P and volume V of steam satisfy the equation P V 1.4 = k where k is a constant. (This is true for adiabatic expansion, that is, expansion in which there is no heat transfer between the cylinder and its surroundings.) Use Exercise 29 to calculate the work done by the engine during a cycle when the steam starts at a pressure of 160  lb/in 2 and a volume of 100  in 3 and expands to a volume of 800  in 3 .

To determine

To calculate:

The work done by the engine during a cycle using exercise 29

Explanation

1) Concept:

The work is calculated by using the formula W=abf(x)dx

2) Given:

The pressure and volume satisfies the equation PV1.4=k and the initial pressure  P=160 lb/in2 and the initial and final volumes are V1=100 in3,  V2=800 in3

3) Calculation:

Convert inch to feet by using the relation 12 inch = 1 feet,  so 144 in2=1 ft2  and 1728 in3=1 ft3

At the start P=160 lb/in2=160·144 lb/ft2

V1=100 in3=1001728ft3,  V2=8001728ft3 But

PV1.4=k  So

k=160·144 10017281.4=2304010017281

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