Solucionario

Review Problems


1-121 Cold water is to be heated in a 1200-W teapot. The time needed to heat the water is to be determined.
Assumptions 1 Steady operating conditions exist. 2 Thermal properties of the teapot and the water are constant. 3 Heat loss from the teapot is negligible.
Properties The average specific heats are given to be 0.6 kJ/kg.(C for the teapot and 4.18 kJ/kg.(C for water.Analysis We take the teapot and the water in it as our system that is a closed system (fixed mass). The energy balance in this case can be expressed as
[pic]
Then the amount of energy needed to raise the temperature of water and the teapot from 18(C to 96(C is
[pic]
The 1500 W electric heating unit will supply energy at a rate of 1.2 kW or 1.2 kJ per second. Therefore, the time neededfor this heater to supply 853 kJ of heat is determined from
[pic]
Discussion In reality, it will take longer to accomplish this heating process since some heat loss is inevitable during the heating process.
1-122 The duct of an air heating system of a house passes through an unheated space in the attic. The rate of heat loss from the air in the duct to the attic and its cost under steadyconditions are to be determined.
Assumptions 1 Air is an ideal gas since it is at a high temperature and low pressure relative to its critical point values of -141(C and 3.77 MPa. 2 Steady operating conditions exist since there is no change with time at any point and thus [pic]. 3 The kinetic and potential energy changes are negligible, [pic]. 4 Constant specific heats at room temperature can be usedfor air. This assumption results in negligible error in heating and air-conditioning applications.
Properties The gas constant of air is R = 0.287 kJ/kg.K (Table A-1). The specific heat of air at room temperature is Cp = 1.007 kJ/kg·C (Table A-15).
Analysis We take the heating duct as the system. This is a control volume since mass crosses the system boundary during the process. There is onlyone inlet and one exit and thus [pic]. Then the energy balance for this steady-flow system can be expressed in the rate form as
[pic]
The density of air at the inlet conditions is determined from the ideal gas relation to be
[pic]
The cross-sectional area of the duct is
[pic]
Then the mass flow rate of air through the duct and the rate of heat loss become
[pic]
and
[pic]
or 1760kJ/h. The cost of this heat loss to the home owner is
[pic]
Discussion The heat loss from the heating ducts in the attic is costing the homeowner 1.2 cents per hour. Assuming the heater operates 2,000 hours during a heating season, the annual cost of this heat loss adds up to $24. Most of this money can be saved by insulating the heating ducts in the unheated areas.

1-123
"GIVEN"
L=4 "[m]"D=0.2 "[m]"
P_air_in=100 "[kPa]"
T_air_in=65 "[C]"
"Vel=3 [m/s], parameter to be varied"
T_air_out=60 "[C]"
eta_furnace=0.82
Cost_gas=0.58 "[$/therm]"

"PROPERTIES"
R=0.287 "[kJ/kg-K], gas constant of air"
C_p=CP(air, T=25) "at room temperature"

"ANALYSIS"
rho=P_air_in/(R*(T_air_in+273))
A_c=pi*D^2/4
m_dot=rho*A_c*Vel
Q_dot_loss=m_dot*C_p*(T_air_in-T_air_out)*Convert(kJ/s, kJ/h)Cost_HeatLoss=Q_dot_loss/eta_furnace*Cost_gas*Convert(kJ, therm)*Convert($, cents)

|Vel [m/s] |CostHeatLoss [Cents/h] |
|1 |0.3934 |
|2 |0.7868 |
|3 |1.18 |
|4 |1.574 |
|5 |1.967 ||6 |2.361 |
|7 |2.754 |
|8 |3.147 |
|9 |3.541 |
|10 |3.934 |


[pic]
1-124 Water is heated from 16°C to 43°C by an electric resistance heater placed in the water pipe as it flows through a...