It gas in a cylinder is maintained at a constant temperature T, the pressure P is related to the volume V by a formula of the form P=- nRT V-nb Find dP dV Choose the correct answer below. dP O A. = dV dP OB. dV O c. dP dv dV nRT 2an² (V-nb)² V³ nRT an² V-nb V² nRT (V-nb)² sk my instructor + nRT an V-nb v² 2an² V3 an² V² in which a, b, n, and R are constants. Clear all Check answer A 901 406 PM
It gas in a cylinder is maintained at a constant temperature T, the pressure P is related to the volume V by a formula of the form P=- nRT V-nb Find dP dV Choose the correct answer below. dP O A. = dV dP OB. dV O c. dP dv dV nRT 2an² (V-nb)² V³ nRT an² V-nb V² nRT (V-nb)² sk my instructor + nRT an V-nb v² 2an² V3 an² V² in which a, b, n, and R are constants. Clear all Check answer A 901 406 PM
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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![**Problem Statement:**
If gas in a cylinder is maintained at a constant temperature \( T \), the pressure \( P \) is related to the volume \( V \) by a formula of the form:
\[
P = \frac{nRT}{V - nb} - \frac{an^2}{V^2}
\]
where \( a \), \( b \), \( n \), and \( R \) are constants.
**Task:**
Find \(\frac{dP}{dV}\).
**Multiple Choice Options:**
A. \(\frac{dP}{dV} = \frac{nRT}{(V - nb)^2} - \frac{2an^2}{V^3}\)
B. \(\frac{dP}{dV} = \frac{nRT}{V - nb} + \frac{an^2}{V^2}\)
C. \(\frac{dP}{dV} = -\frac{nRT}{(V - nb)^2} + \frac{2an^2}{V^3}\)
D. \(\frac{dP}{dV} = \frac{nRT}{V - nb} - \frac{an^2}{V^2}\)
**Solution Strategy:**
To find \(\frac{dP}{dV}\), apply the derivative rules to each component of the expression for \( P \). Specifically, apply the power rule and chain rule as needed to find the derivatives of the respective terms.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F10b1f275-2c41-4985-b23a-aa3382c0d493%2F0cd6dbde-1ad4-407a-a52e-2ebb8023981e%2F6j5a5wr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
If gas in a cylinder is maintained at a constant temperature \( T \), the pressure \( P \) is related to the volume \( V \) by a formula of the form:
\[
P = \frac{nRT}{V - nb} - \frac{an^2}{V^2}
\]
where \( a \), \( b \), \( n \), and \( R \) are constants.
**Task:**
Find \(\frac{dP}{dV}\).
**Multiple Choice Options:**
A. \(\frac{dP}{dV} = \frac{nRT}{(V - nb)^2} - \frac{2an^2}{V^3}\)
B. \(\frac{dP}{dV} = \frac{nRT}{V - nb} + \frac{an^2}{V^2}\)
C. \(\frac{dP}{dV} = -\frac{nRT}{(V - nb)^2} + \frac{2an^2}{V^3}\)
D. \(\frac{dP}{dV} = \frac{nRT}{V - nb} - \frac{an^2}{V^2}\)
**Solution Strategy:**
To find \(\frac{dP}{dV}\), apply the derivative rules to each component of the expression for \( P \). Specifically, apply the power rule and chain rule as needed to find the derivatives of the respective terms.
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