The roof of a house consists of a 15-cm-thick concrete slab (k = 2 W/m·K) that is 15 m wide and 20 m long. The convection heat transfer coefficients on the inner and outer surfaces of the roof are 5 and 12 W/m2·K, respectively. On a clear winter night, the ambient air is reported to be at 10°C, while the night sky temperature is 100 K. The house and the interior surfaces of the wall are maintained at a constant temperature of 20°C. The emissivity of both surfaces of the concrete roof is 0.9. Considering both radiation and convection heat transfers, determine the rate of heat transfer through the roof, and the inner surface temperature of the roof. If the house is heated by a furnace burning natural gas with an efficiency of 80 percent, and the price of natural gas is $1.20/ therm (1 therm = 105,500 kJ of energy content), determine the money lost through the roof that night during a 14-h period.
Energy transfer
The flow of energy from one region to another region is referred to as energy transfer. Since energy is quantitative; it must be transferred to a body or a material to work or to heat the system.
Molar Specific Heat
Heat capacity is the amount of heat energy absorbed or released by a chemical substance per the change in temperature of that substance. The change in heat is also called enthalpy. The SI unit of heat capacity is Joules per Kelvin, which is (J K-1)
Thermal Properties of Matter
Thermal energy is described as one of the form of heat energy which flows from one body of higher temperature to the other with the lower temperature when these two bodies are placed in contact to each other. Heat is described as the form of energy which is transferred between the two systems or in between the systems and their surrounding by the virtue of difference in temperature. Calorimetry is that branch of science which helps in measuring the changes which are taking place in the heat energy of a given body.
The roof of a house consists of a 15-cm-thick concrete
slab (k = 2 W/m·K) that is 15 m wide and 20 m long.
The
outer surfaces of the roof are 5 and 12 W/m2·K, respectively.
On a clear winter night, the ambient air is reported to be at
10°C, while the night sky temperature is 100 K. The house
and the interior surfaces of the wall are maintained at a constant
temperature of 20°C. The emissivity of both surfaces
of the concrete roof is 0.9. Considering both
convection heat transfers, determine the rate
through the roof, and the inner surface temperature of the
roof.
If the house is heated by a furnace burning natural gas with
an efficiency of 80 percent, and the price of natural gas is $1.20/
therm (1 therm = 105,500 kJ of energy content), determine the
money lost through the roof that night during a 14-h period.
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