7-40
7-119 The thermal efficiency and power output of a gas turbine are given. The rate of fuel consumption of the gas turbine is
to be determined.
Assumptions Steady operating conditions exist.
7-44
7-125 The maximum flow rate of a standard shower head can be reduced from 13.3 to 10.5 L/min by switching to low-flow
shower heads. The amount of oil and money a family of four will save per year by replacing the standard shower heads by
the low-flow ones are to be determined.
Assumptions 1 Steady operating conditions exist. 2 Showers
operate at maximum flow conditions during the entire
shower. 3 Each member of the household takes a 5-min
shower every day.
Shower
Head
13.3 L/min
7-46
This problem can also be solved exactly by integration as follows:
The maximum work will be obtained if a Carnot heat engine is used. The sink temperature of this heat engine will remain
constant at 300 K but the source temperature will be decreasing from 350 K to 300 K. Then the thermal efficiency of the
Carnot heat engine operating between pond and the ambient air can be expressed as
L
T300
HHH
dTdTcmQQ
KkJ/kg4.18kg105
pond
Also,
H
H
HT
T
QW
KkJ/kg 4.18kg 10
300
15
Cth,net
Pond
105 kg
350 K
HE
7-47
7-127 A refrigeration system is to cool bread loaves at a rate of 1200 per hour by refrigerated air at –30C. The rate of heat
removal from the breads, the required volume flow rate of air, and the size of the compressor of the refrigeration system are
is 0.287 kPa.m3/kg.K (Table A-1), and the specific heat of air at the
average temperature of (-30 + -22)/2 = –26C 250 K is cp =1.0
Then the rate of heat removal from the breads as they are cooled from 30C to –10ºC and frozen becomes
–30C
7-49
7-129 A typical heat pump powered water heater costs about $800 more to install than a typical electric water heater. The
number of years it will take for the heat pump water heater to pay for its cost differential from the energy it saves is to be
determined.
Assumptions 1 The price of electricity remains constant. 2 Water is
an incompressible substance with constant properties at room
temperature. 3 Time value of money (interest, inflation) is not
considered.
Analysis The amount of electricity used to heat the water and the
net amount transferred to water are
$0.11/kWh
$350/year
energy ofcost Unit
energy ofcost Total
l)(electrica usedenergy Total
r$100.8/yea=
$0.11/kWh)kWh/year)( (916.0=
Then the money saved per year by the heat pump and the simple payback period become
years3.21=
r$249.2/yea
$800
=
savedMoney
coston installati Additional
=periodpayback Simple
$249.2=
$100.8$350=
pump)heat ofcost (Energy – heater) electric ofcost (Energy =savedMoney
Discussion The economics of heat pump water heater will be even better if the air in the house is used as the heat source for
the heat pump in summer, and thus also serving as an air-conditioner.
Water
Heater
Hot
water
Cold
water
7-50
7-130 Problem 7-129 is reconsidered. The effect of the heat pump COP on the yearly operation costs and the number
of years required to break even are to be considered.
eta=0.95
E_ElectHeater = eta*Cost_ElectHeater /UnitCost “[kWh/year]”
COP=3.3
W_HeatPump = E_HeatPump/COP “[kWh/year]”
“Cost per year to operate the heat pump is”
7-51
2 2.5 3 3.5 4 4.5 5
2.5
3
3.5
4
4.5
COP
NBrkEven [years]
2 2.5 3 3.5 4 4.5 5
50
100
150
200
250
300
350
400
COP
Cost [$/year]
Electric
Heat pump
7-52
7-131 A home owner is to choose between a high-efficiency natural gas furnace and a ground-source heat pump. The
system with the lower energy cost is to be determined.
7-55
7-135 It is to be proven that the COP of all completely reversible refrigerators must be the same when the reservoir
temperatures are the same.
Assumptions The refrigerators operate steadily.
Analysis We begin by assuming that COPA < COPB. When this is the case, a rearrangement of the coefficient of
performance expression yields
L
L
QQ
7-56
7-137 It is to be shown that COPHP = COPR +1 for the same temperature and heat transfer terms.
innet,innet,
innet,
W
W
7-138 ··· 7-142 Design and Essay Problems