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Homework Assignment #3 Solutions  1
ECE 473/TAM 413
Homework Assignment #3 Solutions
1. Equation 5.2.1’s
P
=
!
rT
k
in Kinsler et al. provides one form of the perfect gas law. Another
form is
PV
=
nRT
k
where n is the number of moles and R is the universal gas constant. Obtain a
relationship between r, R and the gas’ molecular weight M.
PV
=
nRT
k
and
P
=
!
rT
k
(see Eq. 5.2.1 and Appendix Eq A9.17)
V
=
nRT
k
P
=
nR
P
P
!
r
"
#
$
%
&
’
=
nR
!
r
(
r
=
nR
!
V
m
=
!
V (massof gas)
"
r
=
nR
m
and
M
=
m
n
(molecular weight)
Therefore,
r
=
R
M
or
R
=
rM
2. Problem 5.2.1 in Kinsler et al.
(a)
P
P
o
=
!
!
o
"
#
$
%
&
’
(
=
1
+
s
( )
(
)
1
+
(
s
+
...
=
1
+
(
s
for s<<1, that is,
P
=
P
o
1
+
!
s
( ) =
P
o
+
P
o
!
s
From (5.2.5)
P
!
P
o
=
B
" ! "
o
"
o
#
$
%
&
’
(
,
P
=
P
o
+
B
! " !
o
!
o
#
$
%
&
’
(
=
P
o
+
Bs
,
B
=
!
P
o
Also note from (5.2.6)
p
=
Bs
where
B
=
!
o
"
P
"!
#
$
%
&
’
(
!
o
,
B
=
!
o
"
"!
P
o
!
!
o
#
$
%
&
’
(
)
*
+
,

,
.
/
,
0
,
#
$
%
%
&
’
(
(
!
o
=
)
P
o
!
!
o
#
$
%
&
’
(
) 1
1
#
$
%
&
’
(
!
o
=
)
P
o
(b)
B
=
!
P
o
=
! "
rT
K
( )
, so
B
!
T
K
3. The planet Jupiter has an atmosphere of methane at a temperature of 130˚C. Estimate the
speed of sound there.
Use
c
=
!
rT
k
(from notes)
!
=
1.3
for methane
M = 16.04 for methane
r
=
R
o
M
=
8314 J /(kg
!
K)
16.04
=
518.3 J /(kg
!
T
k
=
273
!
130
=
143K
c
=
1.3 518.3 J /(kg
!
( )
=
310 m /s
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View Full DocumentHomework Assignment #3 Solutions  2
4. Problem 5.4.1 in Kinsler et al. (Hint: think total derivative
d
!
dt
)
Take the total derivative of density with respect to time, where density is a function of time and
space.
d
!
dt
=
"!
"
t
+
"!
"
x
"
x
"
t
+
"!
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 Fall '08
 OBRIAN

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