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5-80
5-106 A sample of a food is burned in a bomb calorimeter, and the water temperature rises by 3.2°C when equilibrium is
established. The energy content of the food is to be determined.
Assumptions 1 Water is an incompressible substance with constant specific heats. 2 Air is an ideal gas with constant
specific heats. 3 The energy stored in the reaction chamber is negligible relative to the energy stored in water. 4 The energy
supplied by the mixer is negligible.
Properties The specific heat of water at room temperature is c = 4.18 kJ/kg·°C (Table A-3). The constant volume specific
heat of air at room temperature is cv = 0.718 kJ/kg·°C (Table A-2).
Analysis The chemical energy released during the combustion of the sample is transferred to the water as heat. Therefore,
disregarding the change in the sensible energy of the reaction chamber, the energy content of the food is simply the heat
transferred to the water. Taking the water as our system, the energy balance can be written as
5-82
5-108 An insulated rigid tank initially contains saturated liquid water and air. An electric resistor placed in the tank is turned
on until the tank contains saturated water vapor. The volume of the tank, the final temperature, and the power rating of the
resistor are to be determined.
Assumptions 1 The tank is stationary and thus the kinetic and potential energy changes are zero. 2 There are no work
interactions. 3 Energy added to the air is neglected.
kJ/kg 46.850
0
1
1
u
x
Analysis (a) We take the contents of the tank as the system. We neglect energy added to the air in our analysis based on the
problem statement. This is a closed system since no mass enters or leaves. Noting that the volume of the system is constant
and thus there is no boundary work, the energy balance for this stationary closed system can be expressed as
kinetic, internal,in Change
system
nsferenergy traNet
outin
EEE
5-83
5-109 A 0.3-L glass of water at 20°C is to be cooled with ice to 5°C. The amount of ice or cold water that needs to be added
to the water is to be determined.
A-3). The specific heat of ice at about 0C is c = 2.11 kJ/kg·°C (Table A-3). The melting temperature and the heat of
fusion of ice at 1 atm are 0C and 333.7 kJ/kg,.
Analysis (a) The mass of the water is
waterice
0
UU
0)]([])C0()C0([ water12iceliquid2solid1 TTmcTmcmhTmc if
m = 0.0546 kg = 54.6 g
Cooling with cold water can be handled the same way. All we need to do is replace the terms for ice by a term for cold
water at 0C:
0
waterwatercold
UU
0.3 L
Ice cubes
5-86
5-112 Two rigid tanks that contain water at different states are connected by a valve. The valve is opened and the two tanks
come to the same state at the temperature of the surroundings. The final pressure and the amount of heat transfer are to be
determined.
Assumptions 1 The tanks are stationary and thus the kinetic and potential energy changes are zero. 2 The tank is insulated
and thus heat transfer is negligible. 3 There are no work interactions.
Analysis We take the entire contents of the tank as the system.
This is a closed system since no mass enters or leaves. Noting
that the volume of the system is constant and thus there is no
boundary work, the energy balance for this stationary closed
system can be expressed as
energies etc. p otential,
kinetic, internal,in Change
sy stem
mass and work,heat,by
nsferenergy traNet
outin
EEE
H2O
400 kPa
H2O
200 kPa
B
A
Q
5-88
010 20 30 40 50
1950
2000
2050
2100
2150
2200
2250
2300
Tfinal [C]
Qout [kJ]
0 5 10 15 20 25 30 35 40 45 50
0
3
6
9
12
15
Tfinal [C]
Pfinal [kPa]
5-89
5-114 An insulated cylinder is divided into two parts. One side of the cylinder contains N2 gas and the other side contains
He gas at different states. The final equilibrium temperature in the cylinder when thermal equilibrium is established is to be
determined for the cases of the piston being fixed and moving freely.
Assumptions 1 Both N2 and He are ideal gases with constant specific heats. 2 The energy stored in the container itself is
negligible. 3 The cylinder is well-insulated and thus heat transfer is negligible.
Properties The gas constants and the constant volume specific heats are R = 0.2968 kPa.m3/kg.K is c
v
= 0.743 kJ/kg·°C for
N2, and R = 2.0769 kPa.m3/kg.K is c
v
= 3.1156 kJ/kg·°C for He (Tables A-1 and A-2)
kg 0.7691
K 313K/kgmkPa 2.0769
m 1kPa 500
3
3
He
1
11
He
RT
P
m
V
Taking the entire contents of the cylinder as our system, the 1st law relation can be written as
He12N12
HeN
energies etc. potential,
kinetic, internal,in Change
system
mass and work,heat,by
nsferenergy traNet
outin
)]([)]([0
0
2
2
TTmcTTmc
UUU
EEE
vv
Substituting,
0C40CkJ/kg 3.1156kg 0.7691C012CkJ/kg 0.743kg 4.287 ff TT
It gives
Tf = 85.7C
where Tf is the final equilibrium temperature in the cylinder.
120C
40C
5-90
5-115 An insulated cylinder is divided into two parts. One side of the cylinder contains N2 gas and the other side contains
He gas at different states. The final equilibrium temperature in the cylinder when thermal equilibrium is established is to be
determined for the cases of the piston being fixed and moving freely.
Assumptions 1 Both N2 and He are ideal gases with constant specific heats. 2 The energy stored in the container itself,
5-92
mPist
[kg]
T2,neglPist
[C]
T2,withPist
[C]
1
2
3
4
5
6
7
8
9
10
85.65
85.65
85.65
85.65
85.65
85.65
85.65
85.65
85.65
85.65
85.29
84.96
84.68
84.43
84.2
83.99
83.81
83.64
83.48
83.34
83
83.5
84
84.5
85
85.5
86
mPist [kg]
T2 [C]
Without piston
With piston
5-93
5-117 A piston-cylinder device initially contains saturated liquid water. An electric resistor placed in the tank is turned on
until the tank contains saturated water vapor. The volume of the tank, the final temperature, and the power rating of the
resistor are to be determined.
Assumptions 1 The cylinder is stationary and thus the kinetic and potential energy changes are zero. 2 There are no work
kPa 67.198
0
1
1
P
x
Analysis (a) We take the contents of the cylinder as the system. This is a closed system since no mass enters or leaves.
Noting that the volume of the system is constant and thus there is no boundary work, the energy balance for this stationary
5-95
5-119 A piston-cylinder device contains an ideal gas. An external shaft connected to the piston exerts a force. For an
isothermal process of the ideal gas, the amount of heat transfer, the final pressure, and the distance that the piston is
displaced are to be determined.
Assumptions 1 The kinetic and potential energy changes are
negligible,
ke pe 0
. 2 The friction between the piston and the
(b) The relation for the isothermal work of an ideal gas may be used to determine the final volume in the cylinder. But we
first calculate initial volume
3
2
2
m) (0.12
D
W
