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.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffdea5bec-e634-4619-8e5f-d35b2a241bce%2Fa810d52f-2b7d-48e9-bc57-4e282f44775e%2F4s9l7xb_processed.png&w=3840&q=75)
Transcribed Image Text: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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