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A certain quantity of gas occupies a volume of 20 cm³ at a pressure of 1 atmosphere. The gas expands without the addition of heat, so, for some constant k, its pressure, P, and volume, V, satist the relation PV¹.4 = k (a) Find the rate of change of pressure with volume. Give units. (b) The volume is increasing at 2 cm³/min when the volume is 30 cm³. At that moment, is the pressure increasing or decreasing? How fast? Give units.

A certain quantity of gas occupies a volume of 20 cm³ at a pressure of 1 atmosphere. The gas expands without the addition of heat, so, for some constant k, its pressure, P, and volume, V, satist the relation PV¹.4 = k (a) Find the rate of change of pressure with volume. Give units. (b) The volume is increasing at 2 cm³/min when the volume is 30 cm³. At that moment, is the pressure increasing or decreasing? How fast? Give units.

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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A certain quantity of gas occupies a volume of 20 cm³ at a pressure of 1 atmosphere. The gas expands without the addition of heat, so, for some constant \( k \), its pressure, \( P \), and volume, \( V \), satisfy the relation \[ PV^{1.4} = k \] (a) Find the rate of change of pressure with volume. Give units. (b) The volume is increasing at 2 cm³/min when the volume is 30 cm³. At that moment, is the pressure increasing or decreasing? How fast? Give units.
Transcribed Image Text:A certain quantity of gas occupies a volume of 20 cm³ at a pressure of 1 atmosphere. The gas expands without the addition of heat, so, for some constant \( k \), its pressure, \( P \), and volume, \( V \), satisfy the relation \[ PV^{1.4} = k \] (a) Find the rate of change of pressure with volume. Give units. (b) The volume is increasing at 2 cm³/min when the volume is 30 cm³. At that moment, is the pressure increasing or decreasing? How fast? Give units.
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