Problem 4.8
[Difficulty: 2]
Given:
Data on air compression process
Find:
Work done
Solution:
Basic equation
δ
wp
d
v
⋅
=
Assumptions:
1) Adiabatic
2) Frictionless process
δ
w = pdv
p
1
1 atm
⋅
=
p
2
4 atm
⋅
=
T
1
20 °C
=
T
1
293 K
=
Given data
From Table A.6
R
286.9
J
kg K
⋅
⋅
=
and
k
1.4
=
Before integrating we need to relate p and v.
An adiabatic frictionless (reversible) process is isentropic, which for an ideal gas gives
pv
k
⋅
C
=
where
k
c
p
c
v
=
δ
d
v
⋅
=
Cv
k
−
⋅
dv
⋅
=
Integrating
w
C
k1
−
v
2
1k
−
v
2
−
−
⎛
⎝
⎞
⎠
⋅
=
1
−
()
p
2
v
2
k
⋅
v
2
−
p
1
v
1
k
⋅
v
2
−
⋅
−
⎛
⎝
⎞
⎠
⋅
=
w
R
−
T
2
T
1
−
⋅
=
RT
1
⋅
−
T
2
T
1
1
−
⎛
⎜
⎝
⎞
⎠
⋅
=
(1)
But
k
⋅
C
=
means
p
1
v
1
k
⋅
p
2
v
2
k
⋅
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 Fall '07
 Lear
 Fluid Mechanics

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