The north wall of an electrically heated home is 20ft long, 10ft high, and 1ft thick and is made of brick whose thermal conductivity is k = 0.42 Btu/h . ft . ∘ F . On a certain winter night, the temperatures of the inner and the outer surfaces of the wall are measured to be at about 62 ∘ F and 25 ∘ F, respectively, for a period of 8 h. Determine (a) the rate of heat loss through the wall that night and (b) the cost of that heat loss to the homeowner if cost of electricity is $0.07/kWh.
The north wall of an electrically heated home is 20ft long, 10ft high, and 1ft thick and is made of brick whose thermal conductivity is
k
=
0.42
Btu/h
.
ft
.
∘
F
.
On a certain winter night, the temperatures of the inner and the outer surfaces of the wall are measured to be at about
62
∘
F
and
25
∘
F,
respectively, for a period of 8 h. Determine (a) the rate of heat loss through the wall that night and (b) the cost of that heat loss to the homeowner if cost of electricity is $0.07/kWh.
3. A lumped system with a volume of 0.003 m³ and a surface area of 0.08 m² is made of a material with density of 3800 kg/m³, thermal conductivity of 300 W/m K, and specific heat of 200 J/kg K. If the system is exposed to a convection environment with h = 60 W/m2 K, what is the approximate time it will take for this system to reach equilibrium with the environment? Express your answer in minutes.
The inner and outer surfaces of a 0.5-cm-thick 2-m × 2-m window glass in winter are 15°C and 6°C, respectively. If the thermal conductivity of the glass is 0.78 W/m·°C, determine the amount of heat loss, in kJ, that occurs through the glass over a period of 10 h. What would your answer be if the glass were 1 cm thick?
The roof of an electrically heated home is 12m long, 16m wide, and 0.50m thick, and is made of a flat layer concrete whose thermal conductivity is k=0.8W/m 2 ·°C. The temperature of the inner and outer surfaces of the roof one night are measured to be 12°C and 1°C, respectively, for a period of 12 hours. Determine a) the rate of heat loss through the roof that night b) the cost of that heat loss to the home owner if the cost of electricity is $0.14/kWh.
Chapter 1 Solutions
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