Physics 2C Summer Session I
Quiz #3
Multiple Choice.
Choose the answer that best completes the
statement or answers the question.
1
. An ideal Carnot engine operates between
52
°
C
and
269
°
C
with a heat
input of
250
J
per cycle. Assuming that the acceleration due to gravity is
g
=
10
m=s
2
;
how many cycles are required to lift a
400
g
rock
50
m
?
A)
1
B)
2
C)
4
D)
5
E)
8
The e¢ ciency of this engine is given by
e
= 1
°
T
c
T
h
= 1
°
52 + 273
269 + 273
=
:
4
:
Hence the work output per cycle is
100
J:
The work required to lift a
400
g
rock
50
m
is
200
J
. Hence
2
cycles are required to lift the rock.
!
B
2
. Given that the gas in problem 1 expands by a factor of
5 : 1
during the
isothermal expansion process at
T
= 269
°
C;
how many moles of an inert gas
are required in the Carnot cycle of problem 1 to produce the
250
J
per cycle?
A)
:
086
moles
B)
:
098
moles
C)
:
112
moles
D)
:
136
moles
E)
:
156
moles
The net work by the gas in a Carnot cycle is given by
W
=
nRT
h
ln
V
B
=V
A
°
nRT
c
ln
V
C
=V
D
;
where
V
B
=V
A
is the expansion ratio during the isothermal expansion process at
T
=
T
h
. The expansion ratio
V
C
=V
D
for the expansion ratio at
T
=
T
c
is found
from
T
h
V
°
±
1
B
=
T
c
V
°
±
1
C
T
h
V
°
±
1
A
=
T
c
V
°
±
1
D
V
B
=V
A
=
V
C
=V
D
:
Hence the expansion ratios are equal and
W
=
nR
(
T
h
°
T
c
) ln
V
B
=V
A
!
250 =
n
(8
:
314) (217) ln 5
n
=
250
=
((8
:
314) (217) ln 5) =
:
086
moles
!
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 Summer '09
 Hicks
 Acceleration, Heat, isothermal expansion process, ln VB =VA, Qh Qc COP, VC =VD, nRTc ln VC

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