If the pressure P applied to a gas is increased while the gas is held at a constant temperature, then the volume V of the gas will decrease. The rate of change of the volume of gas with respect to the pressure is proportional to the reciprocal of the square of the pressure. Which of the following is a differential equation that could describe this relationship? V = , where k is a positive constant. A AP dP p2 ,where k is a positive constant. AP dP = , where k is a negative constant. dP dV D where k is a negative constant.

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...
Question
If the pressure P applied to a gas is increased while the gas is held at a constant temperature, then the volume V of the gas will decrease. The rate of change of the volume of gas with
respect to the pressure is proportional to the reciprocal of the square of the pressure. Which of the following is a differential equation that could describe this relationship?
A
V = where k is a positive constant.
p2
AP
= , where k is a positive constant.
B
, where k is a negative constant.
dP
p2
D
dP
where k is a negative constant.
AP
Transcribed Image Text:If the pressure P applied to a gas is increased while the gas is held at a constant temperature, then the volume V of the gas will decrease. The rate of change of the volume of gas with respect to the pressure is proportional to the reciprocal of the square of the pressure. Which of the following is a differential equation that could describe this relationship? A V = where k is a positive constant. p2 AP = , where k is a positive constant. B , where k is a negative constant. dP p2 D dP where k is a negative constant. AP
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