To solve this problem, we can use the formula for heat transfer through a material:
Q = (k * A * ΔT) / L
where:
Q is the heat transferred (in Watts)
k is the thermal conductivity of the material (in kW/m・°C)
A is the surface area of the material (in m²)
ΔT is the temperature difference between the inside and outside (in °C)
L is the thickness of the material (in m)
First, let's calculate the surface area of the walls and roof of the house. Assuming the house is a rectangular prism, we can calculate the surface area using the formula:
A = 2 * (length * width + length * height + width * height)
Given the dimensions in the figure, let's assume the length = 10m, width = 6m, and height = 4m.
A = 2 * (10 * 6 + 10 * 4 + 6 * 4) = 212 m²
Next, let's calculate the temperature difference:
ΔT = inside temperature - outside temperature = 25.0°C - 0.0°C = 25.0°C
Now, let's calculate the volume of gas burned each day to maintain the inside temperature:
Q = (k * A * ΔT) / L
Q = (4.8 * 10^4 kW/m・°C * 212 m² * 25.0°C) / (0.21 m)
Q = 2,545,714.29 kW
Since the energy released per cubic meter of gas burned is given as 9300 kcal/m^3, we need to convert the units to kW:
1 kcal = 4.184 kJ
1 J = 1 W・s
So, 9300 kcal/m^3 = (9300 * 4.184) kJ/m^3 = 38815.2 kJ/m^3 = 38.8152 MJ/m^3 = 38.8152 * 10^3 kW・s/m^3
Now, let's calculate the volume of gas burned each day:
Volume of gas burned = Energy required / Energy released per cubic meter
Volume of gas burned = Q / (38.8152 * 10^3 kW・s/m^3)
Volume of gas burned = 2,545,714.29 kW / (38.8152 * 10^3 kW・s/m^3) = 65.54 m^3
Therefore, approximately 65.54 cubic meters of gas must be burned each day to maintain an inside temperature of 25.0°C when the outside temperature is 0.0°C.
The average thermal conductivity of the walls (including
windows) and roof of a house in Figure P11.32 is
4.8 � 10�4 kW/m� °C, and their average thickness is
21.0 cm. The house is heated with natural gas, with a heat
of combustion (energy released per cubic meter of gas
burned) of 9300 kcal/m3. How many cubic meters of gas
must be burned each day to maintain an inside temperature of 25.0°C if the outside temperature is 0.0°C?
Disregard radiation and energy loss by heat through the
ground.
1 answer