2.18 Case Study: Torricelli’s Law

By the time you complete the CSC, you should know
ExamplesFor a given quantity of gas, Boyle's Law states that the pressure exerted by the gas and the volume it takes up are inversely proportional to each other; that is, P = C/V; or equivalently, PV = C. Assume that the volume changes over time, so V is a function of t. Find the rate of change of the pressure with respect to time in two different ways: in terms of V, dV/dt only, and in terms of P, dV/dt only.
Assume that the pressure exerted by the gas is modeled by the equation
A gas occupies 6.52 liters at a pressure of 0.92 atmospheres. Determine the volume if the pressure is increased to 1.44 atmospheres. If the pressure change is linear and occurs over a period of 5 seconds, what is the instantaneous rate of change of the volume with respect to time at 2 seconds? AppletsFunction Grapher
VideosSee short videos of worked problems for this section.
QuizExercisesSee Exercises for 2.18 Case Study: Toricelli's Law (PDF).Work online to solve the exercises for this section, or for any other section of the textbook. 
Resources on the WebInformation on NewtonBiographical data from St. Andrew's University's Web site Excerpt from W.W. Rouse Ball's "A Short Account of the History of Mathematics"
Information on Leibniz
Calculus Applications

2.17 Related Rates  Table of Contents  3.1 Modeling with Differential Equations 
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Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel