ME 309 Fall 2008
Section 2 (Merkle)
Homework # 8
Due Mon 15 Sep 2008
Problem 81
A frictionless 3000
N
piston maintains a gas at constant pressure in a
cylinder.
The crosssectional area of the piston is 5200
mm
2
and the atmospheric
pressure acting on this area is 0.1
MPa
. A process occurs in which a paddle wheel
transfers 6800
N
·
m
of work to the gas, 10
kJ
of heat is transferred from the gas, and the
internal energy of the gas decreases by 1
kJ
. Determine the distance (
mm
) moved by the
piston.
Solution
:
Known
:
piston = 3000 N,
p=0.1Mpa (const),
A = 05200
mm
2
,
Paddle wheel work—
6800
n m
Q=10 kJ
Δ
U=1
kJ
.
Find:
Distance piston moves (
mm
)
Sketch
:
Assumptions
:
Perfect gas, all work input to paddle goes into fluid; no change in pe or ke
Analysis
:
Note
:
1
Nm
= 1
J
P
gas
= 100,000 + 3000/5.2e3 = 676,900
N/m
2
Energy equation
Q – W =
Δ
U
gas
Q is removed—sign is negative:
Q = 10,000
J
Work done on system by paddle = 6800
Nm
(=
J
)
Work done by piston against ambient pressure (force times distance)
Note
:
Fluid inside piston pushes against both the piston weight and the ambient
pressure, so the pressure acting is the pressure inside the cylinder.
= p
cyl
A
* d =
Nm
Energy equation:
10,000 + 6800 + 676,900*5.2e3*d = 1000
J
Solve for distance traveled by piston:
= 0.625
m
Piston Travel
:
625
mm
Problem 82
A wellinsulated, 0.3028 m
3
(80gal), electric hotwater heater initially
contains water at 322
K
(120 F). Hot water is withdrawn from the tank at 1.893e4
m
3
/s
(3 gal/min) while cold water at 283
K
(50 F) enters to keep the tank full. The cold water
mixes completely with the water in the tank at each instant. Because of a power outage,
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View Full Documentthere is no energy input to heat the incoming cold water. Estimate the time required for
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 Spring '08
 MERKLE
 Energy, mass flow, exit velocity, Aex

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