Solution Manual for A Concise Introduction to Pure Mathematics, 4th Edition by Martin Liebeck

, Chapter 1 - Section A - Mathcad Solutions
m m m m m m m




1.4 ThemequationmthatmrelatesmdegmFmtomdegmCmis:mt(F)m=m1.8mt(C)m+m32.m Solve
mthism
equationmbymsettingmt(F)m=mt(C).

Guessm solution: tm =m 0
Given m Find(t)m =m −40 Ans.
tm=m 1.8tm+m3
mm



2

F
1.5 Bym definition: Pm =mm Fm=m mass Note:mPressuresmaremi
A g nmgaugempressure.
m 2
mPm=m 3000ba Dm=m4m
m Am = D Am =m 12.566mmm
4 2
r m

Fm =m P gm =m 9.807m massm=m massm =m 384.4mkg Ans.
A m F
2 g
s

1.6 Bymdefinition: Fm =m massg
F
Pm =mm
A
m 2
Pm=m3000at
m mDm=m0.17i Am D Am =m 0.023mi
2
m n = 4 n
ft
Fm =m P gm =m 32.174mmm massm=m massm =m 1000.7mlb Ans.
2 F m
A sec
g


1.7 Pabsm =m gh m+mPatm

gm m
m =m 13.535m gm =m 9.832 hm =m 56.38cm
m
3 2
cm  s
ProcessmEngineeringmChanne




Patmm =m 101.78kP Pabsm =m gh m+mPat mPabsm =m 176.808mkP Ans.
a m a
lm@ProcessEng




gm f
1.8 m =m 13.535m gm =m 32.243m hm =m 25.62i
3 t
cm s n
2

,mPatmm =m 29.86in_H Pabsm =m gh m+mPat mPabsm =m 27.22mpsi Ans.
g m a

1

, gm
1.10 Assumemthemfollowing: m =m 13.5m gm =m 9.8m
3 m
cm s
2
P
Pm =m 400ba hm =
g hm =m 302.3m Ans.
r m

1.11 Them forcem onm am springm ism describedm by:m Fm=m Ksm xm wherem Ksm ism them spri
ngmconstant.m FirstmcalculatemKmbasedmonmthemearthmmeasurementmthe
nmgMarsmbasedmonmspringmmeasurementmonmMars.
OnmEarth:
m
Fm =m massgm =m K massm =m 0.40k gm =m 9.8 xm =m 1.08cm
2
x 1 s

gmFm =m 3.924mN Ksm =m Ksm =m 363.333m
Fm =m massg F N m

Onm Mars: x
FMarsm =m Kx
xm =m 0.40cm −m
FMarsm =m 4mm103 mmK
g
FM mmK
=mmmm
arsmMars gMarsm =m 0.0 Ans.
mass kg
1

dm MP dm MPm
1.12 Given: Pm =m −gm and: Substituting: Pm =m −m 
dz m RT
m gmdz RT
=

P z
 Denver 1m  Denver mMgm
Separatingm variablesm andm integrating  dPm =m − dz
 P 
: P  m 
RTm

sea 0

 PDenver
= −Mg zDenver
m
Afterm integrating: ln
ProcessmEngineeringmChanne




 Psea  RT


Takingmthemexponentialmofmbothmside m−mMgmz 
s
 RT Denver

andmrearranging: PDenverm Pseae
lm@ProcessEng




=
Pseam =m 1atm