1.7 Pabs ρg⋅h⋅Patm
+=
1.8 ρ13.535 gm
cm3
⋅:= g 32.243 ft
s2
⋅:= h 25.62in:=
Chapter 1 – Section A – Mathcad Solutions
1.4 The equation that relates deg F to deg C is: t(F) = 1.8 t(C) + 32. Solve this
equation by setting t(F) = t(C).
Guess solution: t0:=
1.5 By definition: PF
A
=F mass g⋅=Note: Pressures are in
gauge pressure.
1.6 By definition: PF
A
=F mass g⋅=
1
1.12 Given: zP
d
dρ− g⋅=and: ρMP⋅
RT⋅
=Substituting: zP
d
d
MP⋅
RT⋅
−g⋅=
Taking the exponential of both sides
and rearranging: PDenver Psea e
M−g⋅
RT⋅zDenver
⋅
⎛
⎜
⎝⎞
⎠
⋅=
1.11 The force on a spring is described by: F = Ks x where Ks is the spring
constant. First calculate K based on the earth measurement then gMars
based on spring measurement on Mars.
On Earth:
2
1.14 costbulb 5.00dollars
1000hr 10⋅hr
day
:= costelec 0.1dollars
kW hr⋅10⋅hr
day 70⋅W:=
1.15 D 1.25ft:= mass 250lbm
:= g 32.169 ft
s2
:=
1.13 The same proportionality applies as in Pb. 1.11.
3
1.18 mass 1250kg:= u40
m
s
:=
1.19 Wdot mass g⋅∆h⋅
time 0.91⋅0.92⋅=
Patm 30.12in_Hg:= Aπ
⋅:= A 1.227ft2
=
1.16 D 0.47m:= mass 150kg:= g 9.813 m
s2
:=
Patm 101.57kPa:= Aπ
4D2
⋅:= A 0.173m2
=
4
1.22
25.00
b)The electrical energy can directly be converted to other forms of energy
whereas the coal and gasoline would typically need to be converted to heat
and then into some other form of energy before being useful.
5
1.24 Use the Matcad genfit function to fit the data to Antoine’s equation.
The genfit function requires the first derivatives of the function with
First derivative of the function with respect to parameter A
First derivative of the function with respect to parameter B
First derivative of the function with respect to parameter C
18.5−
11.8
52.1
75.5
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎝
⎞
⎟
⎟
⎟
⎟
⎟
⎠
3.18
16.9
89.5
187
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎝
⎞
⎟
⎟
⎟
⎟
⎟
⎠
6
Array of functions used by Mathcad. In this case, a0 = A, a1 = B and a2 = C.
Guess values of parameters
⎜
⎜
⎜
⎜
exp a0a1
Ta
2
+
−
⎛
⎜
⎝
⎞
⎠
⎡
⎢
⎤
⎥
Apply the genfit function
⎜
⎜
⎜
Compare fit with data.
150
200
T
To find the normal boiling point, find the value of T for which Psat = 1 atm.
7
This is an open-ended problem. The strategy depends on age of the child,
c)
C280000 dollars
yr
:=C116000 dollars
yr
:=t22000:=t11970:=
b)
i5%:=C10.35 dollars
gal
:=t22000:=t11970:=
a)
1.25
8