EXAMPLE 2 The pressure P (in kilopascals), volume V (in liters), and temperature T (in kelvins) of a mole of an ideal gas are related by the equation PV = 8.317. Find the rate at which the pressure is changing when the temperature is 300 K and increasing at a rate of 0.3 K/s and the volume is 200 L and increasing at a rate of 0.3 L/s. SOLUTION If t represents the time elapsed in seconds, then at the given instant, we have T = 300, dT/dt = 0.3, V = 200, dv/dt = 0.3. Since P = 8.31, the Chain Rule gives the following. (Round your final answer to five decimal places.) ap dT aT dt ap dv av dt dP dt 8.31 dT dv V dt dt 8.31(300) 2002 8.31 200 The pressure is decreasing at a rate, rounded to three decimal places, of about kPA/s.

EXAMPLE 2 The pressure P (in kilopascals), volume V (in liters), and temperature T (in kelvins) of a mole of an ideal gas are related by the equation PV = 8.317. Find the rate at which the pressure is changing when the temperature is 300 K and increasing at a rate of 0.3 K/s and the volume is 200 L and increasing at a rate of 0.3 L/s. SOLUTION If t represents the time elapsed in seconds, then at the given instant, we have T = 300, dT/dt = 0.3, V = 200, dv/dt = 0.3. Since P = 8.31, the Chain Rule gives the following. (Round your final answer to five decimal places.) ap dT aT dt ap dv av dt dP dt 8.31 dT dv V dt dt 8.31(300) 2002 8.31 200 The pressure is decreasing at a rate, rounded to three decimal places, of about kPA/s.

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Description: Solve all that is asked in the image EXAMPLE 2 The pressure P (in kilopascals), volume V (in liters), andtemperature T (in kelvins) of a mole of an ideal gas are related by theequation PV = 8.317. Find the rate at which the pressure is changing whent

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.7: Applications

Problem 13EQ

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