(a) Differentiate both sides of the equation above with respect to t to get an equation that relates T, and . dt AP (b) Suppose the temperature of the system is increasing at a rate of one degree C per second, and the volume of the system is decreasing at a rate of 0.2 cubic meters per second. After 12 seconds, the volume of the system is 6 cubic meters, and the temperature is 40 degrees C. What is the instantancous rate of change of the pressure of the system after 12 seconds? Your answer will depend on the unknown constant k.

(a) Differentiate both sides of the equation above with respect to t to get an equation that relates T, and . dt AP (b) Suppose the temperature of the system is increasing at a rate of one degree C per second, and the volume of the system is decreasing at a rate of 0.2 cubic meters per second. After 12 seconds, the volume of the system is 6 cubic meters, and the temperature is 40 degrees C. What is the instantancous rate of change of the pressure of the system after 12 seconds? Your answer will depend on the unknown constant k.

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

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2. Boyle's law gives the relationship
kT
P =
V
where P is the pressure of gas in a system, V is the volume of the gas, T is the temperature, and k
is a constant. In other words, pressure is proportional to temperature and inversely proportional to
volume.
(a) Differentiate both sides of the cquation above with respect to l to get an equation that relates
dT, and dV.
dt
(b) Suppose the temperature of the system is increasing at a rate of one degree C per second, and
the volume of the system is decreasing at a rate of 0.2 cubic meters per second. After 12 seconds,
the volume of the system is 6 cubic meters, and the temperature is 40 degrees C. What is the
instantancous rate of change of the pressure of the system after 12 seconds? Your answer will
depend on the unknown constant k.

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