EML 3100
–
Homework 1
Due Wednesday, January 18
From the Textbook
: Problems 2.40, 2.47, 2.75, 2.82
Problem 5
: Hydrogen gas having an energy content per unit mass of
e
= 120 MJ/kg is stored in a
tank at 200 bar and 25 ºC. The molecular weight of hydrogen is
M
= 2.016 g/gmol, and the
corresponding gas constant is
R
= 4.124 J/gK. The density of hydrogen is described by
𝜌
=
𝑝
𝑍𝑅𝑇
,
where the compressibility factor
Z
corrects for the deviation from ideal gas behavior that occurs
at high pressure. At 200 bar and 25 ºC,
Z
is estimated as 1.130. Determine the product
e
ρ
in units
of [MJ/m
3
], which represents the energy content of the gas per unit volume.
Problem 6
: The sketch below shows a curve in
p

V
coordinates defined by the polytropic
equation
𝑝𝑉
𝑛
=
?
, where
n
and
c
are positive constants. Verify the following related results:
𝑛
=
ln(
𝑝
1
/
𝑝
2
)
ln(
𝑉
2
/
𝑉
1
)
=
ln(
𝑝
2
/
𝑝
1
)
ln(
𝑉
1
/
𝑉
2
)
,
𝑝
?𝑉
2
1
=
𝑝𝑉
ln
𝑉
2
𝑉
1
for
𝑛
= 1,
𝑝
?𝑉
2
1
=
−
1
𝑛 −
1
∆ 𝑝𝑉
for
𝑛 ≠
1,
Where
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 Spring '08
 Sherif
 Thermodynamics, polytropic curve

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