1. Consider the van der Waals equation (1) a (p+ v2) (Vm – b) – RT = 0 V2 т where p, Vm, T, are, respectively, pressure, molar volume, and temperature and R, a, and b are constants. a) Find aVm. ƏT ) by computing the differential of (1) at constant p. b) Find (Vm ) by computing the differential of (1) at constant T. T c) Use the expressions for (Vm) and ( -) and suitable relationships between ƏT dp T partial derivatives to find (). ƏT Vm d) Use the expressions for and ( aVm ƏT ) and suitable relationships between ƏT Vm partial derivatives to find ( aVm T e) Use (), to find (, av2): Find the value of Vm at which both of these deriva- aVm T tives are zero.
1. Consider the van der Waals equation (1) a (p+ v2) (Vm – b) – RT = 0 V2 т where p, Vm, T, are, respectively, pressure, molar volume, and temperature and R, a, and b are constants. a) Find aVm. ƏT ) by computing the differential of (1) at constant p. b) Find (Vm ) by computing the differential of (1) at constant T. T c) Use the expressions for (Vm) and ( -) and suitable relationships between ƏT dp T partial derivatives to find (). ƏT Vm d) Use the expressions for and ( aVm ƏT ) and suitable relationships between ƏT Vm partial derivatives to find ( aVm T e) Use (), to find (, av2): Find the value of Vm at which both of these deriva- aVm T tives are zero.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 54E: Plant Growth Researchers have found that the probability P that a plant will grow to radius R can be...
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I need help with 1e. I know that the answer is 3b but not sure how to do it.
Transcribed Image Text:1. Consider the van der Waals equation
(1)
a
(p+ v2) (Vm – b) – RT = 0
V2
m
where p, Vm, T, are, respectively, pressure, molar volume, and temperature and R,
a, and b are constants.
a) Find
aVm
) by computing the differential of (1) at constant p.
b) Find
) by computing the differential of (1) at constant T.
aVm
T
c) Use the expressions for ().
aVm
and (m) and suitable relationships between
aVm
ƏT
partial derivatives to find ().
ƏT
Vm
d) Use the expressions for ().
др
ƏT
and ().
aVm
ƏT
and suitable relationships between
Vm
partial derivatives to find ()
aVm
T
e) Use (
ap
to find (
Find the value of Vm at which both of these deriva-
av2
T
tives are zero.
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