Rodriguez, Brandon – Homework 29 – Due: Dec 5 2006, 11:00 am – Inst: Andrew J Rader
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MUST CARRY OUT YOUR CALCULA
TIONS TO AT LEAST THREE SIGNIFI
CANT FIGURES. YOUR ANSWER MUST
BE
WITHIN
ONE
PERCENT
OF
THE
CORRECT RESULT TO BE MARKED AS
CORRECT BY THE SERVER.
001
(part 1 of 2) 4 points
Air in the cylinder of a diesel engine at
47
.
8
◦
C is compressed from an initial pres
sure of 1
.
232 atm and of volume of 820 cm
3
to
a volume of 32
.
5 cm
3
.
Assuming that air behaves as an ideal gas
(
γ
= 1
.
40) and that the compression is adia
batic and reversible, find the final pressure.
Correct answer: 113
.
061 atm.
Explanation:
Let :
P
i
= 1
.
232 atm
,
V
i
= 820 cm
3
,
and
V
f
= 32
.
5 cm
3
.
Using the relation
P
i
V
γ
i
=
P
f
V
γ
f
,
we find that
P
f
=
P
i
V
i
V
f
¶
γ
= (1
.
232 atm)
820 cm
3
32
.
5 cm
3
¶
1
.
40
= 113
.
061 atm
002
(part 2 of 2) 4 points
Find the final temperature under the same
assumptions as above.
Correct answer: 893
.
827
◦
C.
Explanation:
Let :
T
i
= 47
.
8
◦
C = 320
.
8 K
.
Since
P V
=
n R T
is always valid during the
process and since no gas escapes from the
cylinder,
P
i
V
i
T
i
=
P
f
V
f
T
f
=
n R
Therefore,
T
f
=
P
f
V
f
P
i
V
i
T
i
=
(113
.
061 atm) (32
.
5 cm
3
)
(1
.
232 atm) (820 cm
3
)
(320
.
8 K)
= 1166
.
83 K
= 893
.
827
◦
C
keywords:
003
(part 1 of 2) 4 points
Helium gas at
T
i
= 32
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 Spring '08
 pedon
 Thermodynamics, Work, Correct Answer, Andrew J Rader

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